Journal articles: 'Weighted regression estimator'

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Kalina, Jan, and Jan Tichavský. "On Robust Estimation of Error Variance in (Highly) Robust Regression." Measurement Science Review 20, no. 1 (February 1, 2020): 6–14. http://dx.doi.org/10.2478/msr-2020-0002.

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AbstractThe linear regression model requires robust estimation of parameters, if the measured data are contaminated by outlying measurements (outliers). While a number of robust estimators (i.e. resistant to outliers) have been proposed, this paper is focused on estimating the variance of the random regression errors. We particularly focus on the least weighted squares estimator, for which we review its properties and propose new weighting schemes together with corresponding estimates for the variance of disturbances. An illustrative example revealing the idea of the estimator to down-weight individual measurements is presented. Further, two numerical simulations presented here allow to compare various estimators. They verify the theoretical results for the least weighted squares to be meaningful. MM-estimators turn out to yield the best results in the simulations in terms of both accuracy and precision. The least weighted squares (with suitable weights) remain only slightly behind in terms of the mean square error and are able to outperform the much more popular least trimmed squares estimator, especially for smaller sample sizes.

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Zhou, Xiaoshuang, Xiulian Gao, Yukun Zhang, Xiuling Yin, and Yanfeng Shen. "Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information." Symmetry 13, no. 12 (December 10, 2021): 2387. http://dx.doi.org/10.3390/sym13122387.

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In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the optimal estimator is obtained. Furthermore, we conduct some simulations to evaluate the performance of our proposed estimators under different symmetric error distributions. Simulation studies further illustrate that both estimators work better than the local linear least square estimator for all the symmetric errors considered except the normal error, and the weighted quantile average estimator performs better than the weighted composite quantile regression estimator in most situations.

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Cai, Zongwu. "REGRESSION QUANTILES FOR TIME SERIES." Econometric Theory 18, no. 1 (February 2002): 169–92. http://dx.doi.org/10.1017/s0266466602181096.

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In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology.

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Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.

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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.

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Rahmawati, Dyah P., I. N. Budiantara, Dedy D. Prastyo, and Made A. D. Octavanny. "Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression." International Journal of Mathematics and Mathematical Sciences 2021 (March 11, 2021): 1–14. http://dx.doi.org/10.1155/2021/6611084.

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Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

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Zhang, Zhengyu. "LOCAL PARTITIONED QUANTILE REGRESSION." Econometric Theory 33, no. 5 (September 19, 2016): 1081–120. http://dx.doi.org/10.1017/s0266466616000293.

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In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006, Econometrica 74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods. First, it is structurally simple and widely applicable to the general model as well as its submodels. Second, both the functional coefficients and their derivatives up to any given order can be estimated. Third, the procedure readily extends to censored data, including fixed or random censoring. A Monte Carlo experiment indicates that the proposed estimator performs well in finite samples. An empirical application is also provided.

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Schreuder, H. T., and Z. Ouyang. "Optimal sampling strategies for weighted linear regression estimation." Canadian Journal of Forest Research 22, no. 2 (February 1, 1992): 239–47. http://dx.doi.org/10.1139/x92-031.

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Our strong effort to find an optimal sampling strategy that was clearly superior to other strategies for a range of linearity conditions and variance structures for linear models showed that several sampling strategies turned out to be equally efficient. Each of these stratified the population to the maximum extent feasible, i.e., used n strata based on a covariate. Which of two ways of stratification to use and how units in each stratum were selected (simple random sampling or sampling with probability proportional to size) did not seem to matter much. Two regression estimators, one considering both probability and variance weights (Ŷgr) and one considering only probability weights (Ŷpi), are preferred estimators with the five efficient sampling selection schemes that select one unit per stratum with either equal or unequal probability sampling. The bootstrap variance estimator is generally the least biased, yet conservative, variance estimator and yields reliable coverage rates with 95% confidence intervals for most populations studied.

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Tao, Li, Lingnan Tai, Manling Qian, and Maozai Tian. "A New Instrumental-Type Estimator for Quantile Regression Models." Mathematics 11, no. 15 (August 4, 2023): 3412. http://dx.doi.org/10.3390/math11153412.

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This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures.

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Glynn, Adam N., and Kevin M. Quinn. "An Introduction to the Augmented Inverse Propensity Weighted Estimator." Political Analysis 18, no. 1 (2010): 36–56. http://dx.doi.org/10.1093/pan/mpp036.

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In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or the outcome regression is misspecified but the other is properly specified. After explaining the AIPW estimator, we conduct a Monte Carlo experiment that compares the finite sample performance of the AIPW estimator to three common competitors: a regression estimator, an inverse propensity weighted (IPW) estimator, and a propensity score matching estimator. The Monte Carlo results show that the AIPW estimator has comparable or lower mean square error than the competing estimators when the propensity score and outcome models are both properly specified and, when one of the models is misspecified, the AIPW estimator is superior.

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Laome, Lilis, I. Nyoman Budiantara, and Vita Ratnasari. "Estimation Curve of Mixed Spline Truncated and Fourier Series Estimator for Geographically Weighted Nonparametric Regression." Mathematics 11, no. 1 (December 28, 2022): 152. http://dx.doi.org/10.3390/math11010152.

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Geographically Weighted Regression (GWR) is the development of multiple linear regression models used in spatial data. The assumption of spatial heterogeneity results in each location having different characteristics and allows the relationships between the response variable and each predictor variable to be unknown, hence nonparametric regression becomes one of the alternatives that can be used. In addition, regression functions are not always the same between predictor variables. This study aims to use the Geographically Weighted Nonparametric Regression (GWNR) model with a mixed estimator of truncated spline and Fourier series. Both estimators are expected to overcome unknown data patterns in spatial data. The mixed GWNR model estimator is then determined using the Weighted Maximum Likelihood Estimator (WMLE) technique. The estimator’s characteristics are then determined. The results of the study found that the estimator of the mixed GWNR model is an estimator that is not biased and linear to the response variable y.

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Shemail, Ayad H., and Mohammed J. Mohammed. "Semi Parametric Logistic Regression Model with the Outputs Representing Trapezoidal Intuitionistic Fuzzy Number." Journal of Economics and Administrative Sciences 28, no. 133 (September 30, 2022): 70–81. http://dx.doi.org/10.33095/jeas.v28i133.2350.

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In this paper, the fuzzy logic and the trapezoidal fuzzy intuitionistic number were presented, as well as some properties of the trapezoidal fuzzy intuitionistic number and semi- parametric logistic regression model when using the trapezoidal fuzzy intuitionistic number. The output variable represents the dependent variable sometimes cannot be determined in only two cases (response, non-response)or (success, failure) and more than two responses, especially in medical studies; therefore so, use a semi parametric logistic regression model with the output variable (dependent variable) representing a trapezoidal fuzzy intuitionistic number. the model was estimated on simulation data when sample sizes 25,50 and 100, as the parametric part was estimated by two methods of estimation, are fuzzy ordinary least squares estimators FOLSE method and suggested fuzzy weighted least squares estimators SFWLSE , while the non-parametric part is estimated by Nadaraya Watson estimation and Nearest Neighbor estimator. The results were the fuzzy ordinary least squares estimators method was better than the suggested fuzzy weighted least squares estimators while, in the non-parametric portion, the Nadaraya Watson estimators had better than Nearest Neighbor estimators to estimate the model

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Luo, Shuanghua, Cheng-yi Zhang, and Meihua Wang. "Composite Quantile Regression for Varying Coefficient Models with Response Data Missing at Random." Symmetry 11, no. 9 (August 21, 2019): 1065. http://dx.doi.org/10.3390/sym11091065.

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Composite quantile regression (CQR) estimation and inference are studied for varying coefficient models with response data missing at random. Three estimators including the weighted local linear CQR (WLLCQR) estimator, the nonparametric WLLCQR (NWLLCQR) estimator, and the imputed WLLCQR (IWLLCQR) estimator are proposed for unknown coefficient functions. Under some mild conditions, the proposed estimators are asymptotic normal. Simulation studies demonstrate that the unknown coefficient estimators with IWLLCQR are superior to the other two with WLLCQR and NWLLCQR. Moreover, bootstrap test procedures based on the IWLLCQR fittings is developed to test whether the coefficient functions are actually varying. Finally, a type of investigated real-life data is analyzed to illustrated the applications of the proposed method.

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Octavanny, Made Ayu Dwi, I. Nyoman Budiantara, Heri Kuswanto, and Dyah Putri Rahmawati. "A New Mixed Estimator in Nonparametric Regression for Longitudinal Data." Journal of Mathematics 2021 (November 15, 2021): 1–12. http://dx.doi.org/10.1155/2021/3909401.

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We introduce a new method for estimating the nonparametric regression curve for longitudinal data. This method combines two estimators: truncated spline and Fourier series. This estimation is completed by minimizing the penalized weighted least squares and weighted least squares. This paper also provides the properties of the new mixed estimator, which are biased and linear in the observations. The best model is selected using the smallest value of generalized cross-validation. The performance of the new method is demonstrated by a simulation study with a variety of time points. Then, the proposed approach is applied to a stroke patient dataset. The results show that simulated data and real data yield consistent findings.

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Kong, Efang, Oliver Linton, and Yingcun Xia. "GLOBAL BAHADUR REPRESENTATION FOR NONPARAMETRIC CENSORED REGRESSION QUANTILES AND ITS APPLICATIONS." Econometric Theory 29, no. 5 (February 25, 2013): 941–68. http://dx.doi.org/10.1017/s0266466612000813.

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This paper is concerned with the nonparametric estimation of regression quantiles of a response variable that is randomly censored. Using results on the strong uniform convergence rate of U-processes, we derive a global Bahadur representation for a class of locally weighted polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. Implications of our results are demonstrated through the study of the asymptotic properties of the average derivative estimator of the average gradient vector and the estimator of the component functions in censored additive quantile regression models.

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Yang, Hojin, Hongtu Zhu, Mihye Ahn, and Joseph G. Ibrahim. "Weighted functional linear Cox regression model." Statistical Methods in Medical Research 30, no. 8 (July 4, 2021): 1917–31. http://dx.doi.org/10.1177/09622802211012015.

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The aim of this paper is to develop a weighted functional linear Cox regression model that accounts for the association between a failure time and a set of functional and scalar covariates. We formulate the weighted functional linear Cox regression by incorporating a comprehensive three-stage estimation procedure as a unified methodology. Specifically, the weighted functional linear Cox regression uses a functional principal component analysis to represent the functional covariates and a high-dimensional Cox regression model to capture the joint effects of both scalar and functional covariates on the failure time data. Then, we consider an uncensored probability for each subject by estimating the important parameter of a censoring distribution. Finally, we use such a weight to construct the pseudo-likelihood function and maximize it to acquire an estimator. We also show our estimation and testing procedures through simulations and an analysis of real data from the Alzheimer’s Disease Neuroimaging Initiative.

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Zhang, Yichong, and Xin Zheng. "Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization." Quantitative Economics 11, no. 3 (2020): 957–82. http://dx.doi.org/10.3982/qe1323.

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In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate‐adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.

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Bhat, S. S., and R. Vidya. "Performance of Ridge Estimators Based on Weighted Geometric Mean and Harmonic Mean." Journal of Scientific Research 12, no. 1 (January 1, 2020): 1–13. http://dx.doi.org/10.3329/jsr.v12i1.40525.

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Ordinary least squares estimator (OLS) becomes unstable if there is a linear dependence between any two predictors. When such situation arises ridge estimator will yield more stable estimates to the regression coefficients than OLS estimator. Here we suggest two modified ridge estimators based on weights, where weights being the first two largest eigen values. We compare their MSE with some of the existing ridge estimators which are defined in the literature. Performance of the suggested estimators is evaluated empirically for a wide range of degree of multicollinearity. Simulation study indicates that the performance of the suggested estimators is slightly better and more stable with respect to degree of multicollinearity, sample size, and error variance.

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Millar, Russell B. "A better estimator of mortality rate from age-frequency data." Canadian Journal of Fisheries and Aquatic Sciences 72, no. 3 (March 2015): 364–75. http://dx.doi.org/10.1139/cjfas-2014-0193.

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The Chapman–Robson and weighted-regression estimators are currently the two preferred methods for estimation of instantaneous mortality, z, from a cross-sectional sample of age-frequency data. They are derived under the assumption of steady-state population dynamics. Here, a new estimator is developed from a population model that explicitly includes annual variability in recruitment. The new estimator is trivial to implement using existing generalized linear mixed model software. It is vastly superior to both the Chapman–Robson and weighted-regression estimators under a wide range of simulation scenarios in which sources of variability include partial recruitment to the fishery, autocorrelated annual recruitment, variability in annual survival, ageing error, and sampling randomness. All estimators produced confidence intervals that had lower actual coverage than their nominal 95% coverage. Nonetheless, the new estimator had the highest actual coverage, and under some scenarios this was achieved with a narrowest confidence interval.

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Lee, Kyuseok. "A weighted Fama-MacBeth two-step panel regression procedure: asymptotic properties, finite-sample adjustment, and performance." Studies in Economics and Finance 37, no. 2 (May 28, 2020): 347–60. http://dx.doi.org/10.1108/sef-08-2019-0322.

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Purpose In a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error. Design/methodology/approach First, asymptotic results for the weighted FMB coefficient estimator are provided. Second, a finite-sample-adjusted standard error estimator is provided. Finally, the performance of the adjusted standard error estimator compared to the true standard error is assessed. Findings It is found that the standard error estimator proposed by Yoon and Lee (2019) is asymptotically consistent, although the finite-sample-adjusted standard error estimator proposed in this study works better and helps to reduce bias. The findings of Yoon and Lee (2019) are confirmed even when the average R2 over time is very small with about 1% or 0.1%. Originality/value The findings of this study strongly suggest that the weighted FMB regression procedure, in particular the finite-sample-adjusted procedure proposed here, is a computationally simple but more powerful alternative to the usual unweighted FMB procedure. In addition, to the best of the authors’ knowledge, this is the first study that presents a formal proof of the asymptotic distribution for the FMB coefficient estimator.

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Nurcahayani, Helida, I. Nyoman Budiantara, and Ismaini Zain. "The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression." Mathematics 9, no. 10 (May 18, 2021): 1141. http://dx.doi.org/10.3390/math9101141.

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Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation.

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Newey, Whitney K. "CONDITIONAL MOMENT RESTRICTIONS IN CENSORED AND TRUNCATED REGRESSION MODELS." Econometric Theory 17, no. 5 (September 25, 2001): 863–88. http://dx.doi.org/10.1017/s0266466601175018.

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Censored and truncated regression models with unknown distribution are important in econometrics. This paper characterizes the class of all conditional moment restrictions that lead to √n-consistent estimators for these models. The semiparametric efficiency bound for each conditional moment restriction is derived. In the case of a nonzero bound it is shown how an estimator can be constructed and that an appropriately weighted version can attain the efficiency bound. These estimators also work when the disturbance is independent of the regressors. The paper discusses combining conditional moment restrictions for more efficient estimation in this case.

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Octavanny, Made Ayu Dwi, I. Nyoman Budiantara, Heri Kuswanto, and Dyah Putri Rahmawati. "Nonparametric Regression Model for Longitudinal Data with Mixed Truncated Spline and Fourier Series." Abstract and Applied Analysis 2020 (December 9, 2020): 1–11. http://dx.doi.org/10.1155/2020/4710745.

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Existing literature in nonparametric regression has established a model that only applies one estimator to all predictors. This study is aimed at developing a mixed truncated spline and Fourier series model in nonparametric regression for longitudinal data. The mixed estimator is obtained by solving the two-stage estimation, consisting of a penalized weighted least square (PWLS) and weighted least square (WLS) optimization. To demonstrate the performance of the proposed method, simulation and real data are provided. The results of the simulated data and case study show a consistent finding.

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De Luca, Giuseppe, and Jan R. Magnus. "Bayesian Model Averaging and Weighted-Average Least Squares: Equivariance, Stability, and Numerical Issues." Stata Journal: Promoting communications on statistics and Stata 11, no. 4 (December 2011): 518–44. http://dx.doi.org/10.1177/1536867x1201100402.

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In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to several practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed, and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model-averaging estimation.

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Oliveira, Thiago Wendling Gonçalves de, Rafael Rubilar, Carlos Roberto Sanquetta, Ana Paula Dalla Corte, and Alexandre Behling. "Simultaneous estimation as an alternative to young eucalyptus aboveground biomass modeling in ecophysiological experiments." Acta Scientiarum. Agronomy 43 (July 5, 2021): e52126. http://dx.doi.org/10.4025/actasciagron.v43i1.52126.

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Accurate forest biomass estimates require the selection of appropriate models of individual trees. Thus, two properties are required in tree biomass modeling: (1) additivity of biomass components and (2) estimator efficiency. This study aimed to develop a system of equations to estimate young eucalyptus aboveground biomass and guarantee additivity and estimator efficiency. Aboveground eucalyptus biomass models were calibrated using four methods: generalized least squares (GLS), weighted least squares (WLS), seemingly unrelated regression (SUR), and weighted seemingly unrelated regression (WSUR). The approaches were compared with regard to performance, additivity, and estimator efficiency. The methods did not differ with regard to the mean biomass estimation; therefore, their performance was similar. The GLS and WLS approaches did not satisfy the additivity principle, as the sum of the biomass components was not equal to total biomass. However, this was not observed with the SUR and WSUR approaches. With regard to estimator efficiency, the WSUR approach resulted in narrow confidence intervals and an efficiency gain of over 20%. The WSUR approach should be used in forest biomass modeling as it resulted in effective estimators while ensuring equation additivity, thus providing an easy and accurate alternative to estimate the initial biomass of eucalyptus stands in ecophysiological models.

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Fransiska, Welly, Sigit Nugroho, and Ramya Rachmawati. "A Comparison of Weighted Least Square and Quantile Regression for Solving Heteroscedasticity in Simple Linear Regression." Journal of Statistics and Data Science 1, no. 1 (March 15, 2022): 19–29. http://dx.doi.org/10.33369/jsds.v1i1.21011.

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Regression analysis is the study of the relationship between dependent variable and one or more independent variables. One of the important assumption that must be fulfilled to get the regression coefficient estimator Best Linear Unbiased Estimator (BLUE) is homoscedasticity. If the homoscedasticity assumption is violated then it is called heteroscedasticity. The consequences of heteroscedasticity are the estimator remain linear and unbiased, but it can cause estimator haven‘t a minimum variance so the estimator is no longer BLUE. The purpose of this study is to analyze and resolve the violation of heteroscedasticity assumption with Weighted Least Square(WLS) and Quantile Regression. Based on the results of the comparison between WLS and Quantile Regression obtained the most precise method used to overcome heteroscedasticity in this research is the WLS method because it produces that is greater (98%).

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Kalina, J., and J. Tichavský. "Statistical learning for recommending (robust) nonlinear regression methods." Journal of Applied Mathematics, Statistics and Informatics 15, no. 2 (December 1, 2019): 47–59. http://dx.doi.org/10.2478/jamsi-2019-0008.

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Abstract We are interested in comparing the performance of various nonlinear estimators of parameters of the standard nonlinear regression model. While the standard nonlinear least squares estimator is vulnerable to the presence of outlying measurements in the data, there exist several robust alternatives. However, it is not clear which estimator should be used for a given dataset and this question remains extremely difficult (or perhaps infeasible) to be answered theoretically. Metalearning represents a computationally intensive methodology for optimal selection of algorithms (or methods) and is used here to predict the most suitable nonlinear estimator for a particular dataset. The classification rule is learned over a training database of 24 publicly available datasets. The results of the primary learning give an interesting argument in favor of the nonlinear least weighted squares estimator, which turns out to be the most suitable one for the majority of datasets. The subsequent metalearning reveals that tests of normality and heteroscedasticity play a crucial role in finding the most suitable nonlinear estimator.

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Yang, Hu, Xinfeng Chang, and Deqiang Liu. "Improvement of the Liu Estimator in Weighted Mixed Regression." Communications in Statistics - Theory and Methods 38, no. 2 (January 2009): 285–92. http://dx.doi.org/10.1080/03610920802192513.

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Liu, Chaolin, Hu Yang, and Jibo Wu. "On the Weighted Mixed Almost Unbiased Ridge Estimator in Stochastic Restricted Linear Regression." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/902715.

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We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. We discuss superiorities of the new estimator under the quadratic bias (QB) and the mean square error matrix (MSEM) criteria. Additionally, we give a method about how to obtain the optimal values of parameterskandw. Finally, theoretical results are illustrated by a real data example and a Monte Carlo study.

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Gösta Andersson, Per. "A conditional perspective of weighted variance estimation of the optimal regression estimator." Journal of Statistical Planning and Inference 136, no. 1 (January 2006): 221–34. http://dx.doi.org/10.1016/j.jspi.2004.06.024.

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Sriliana, Idhia, I. Nyoman Budiantara, and Vita Ratnasari. "A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application." Symmetry 14, no. 12 (December 19, 2022): 2687. http://dx.doi.org/10.3390/sym14122687.

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Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using a mixed estimator in nonparametric regression. The objective of this study was to estimate the nonparametric regression curve for longitudinal data using two combined estimators: truncated spline and local linear. The weighted least square method with a two-stage estimation procedure was used to obtain the regression curve estimation of the proposed model. To account for within-subject correlations in the longitudinal data, a symmetric weight matrix was given in the regression curve estimation. The best model was determined by minimizing the generalized cross-validation value. Furthermore, an application to a longitudinal dataset of the poverty gap index in Bengkulu Province, Indonesia, was conducted to illustrate the performance of the proposed mixed estimator. Compared to the single estimator, the truncated spline and local linear mixed estimator had better performance in longitudinal data modeling based on the GCV value. Additionally, the empirical results of the best model indicated that the proposed model could explain the data variation exceptionally well.

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Tao, Li, Lingnan Tai, and Maozai Tian. "Quantile regression for static panel data models with time-invariant regressors." PLOS ONE 18, no. 8 (August 2, 2023): e0289474. http://dx.doi.org/10.1371/journal.pone.0289474.

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This paper proposes two new weighted quantile regression estimators for static panel data model with time-invariant regressors. The two new estimators can improve the estimation of the coefficients with time-invariant regressors, which are computationally convenient and simple to implement. Also, the paper shows consistency and asymptotic normality of the two proposed estimator for sequential and simultaneous N, T asymptotics. Monte Carlo simulation in various parameters sets proves the validity of the proposed approach. It has an empirical application to study the effects of the influence factors of China’s exports using the trade gravity model.

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Li, Erqian, Jianxin Pan, Manlai Tang, Keming Yu, Wolfgang Karl Härdle, Xiaowen Dai, and Maozai Tian. "Weighted Competing Risks Quantile Regression Models and Variable Selection." Mathematics 11, no. 6 (March 8, 2023): 1295. http://dx.doi.org/10.3390/math11061295.

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The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure.

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You, Jinhong, and Xian Zhou. "ASYMPTOTIC THEORY IN FIXED EFFECTS PANEL DATA SEEMINGLY UNRELATED PARTIALLY LINEAR REGRESSION MODELS." Econometric Theory 30, no. 2 (December 13, 2013): 407–35. http://dx.doi.org/10.1017/s0266466613000352.

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This paper deals with statistical inference for the fixed effects panel data seemingly unrelated partially linear regression model. The model naturally extends the traditional fixed effects panel data regression model to allow for semiparametric effects. Multiple regression equations are permitted, and the model includes the aggregated partially linear model as a special case. A weighted profile least squares estimator for the parametric components is proposed and shown to be asymptotically more efficient than those neglecting the contemporaneous correlation. Furthermore, a weighted two-stage estimator for the nonparametric components is also devised and shown to be asymptotically more efficient than those based on individual regression equations. The asymptotic normality is established for estimators of both parametric and nonparametric components. The finite-sample performance of the proposed methods is evaluated by simulation studies.

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Marx, Brian D., and Eric P. Smith. "Weighted Multicollinearity in Logistic Regression: Diagnostics and Biased Estimation Techniques with an Example from Lake Acidification." Canadian Journal of Fisheries and Aquatic Sciences 47, no. 6 (June 1, 1990): 1128–35. http://dx.doi.org/10.1139/f90-131.

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An historical data set from the Adirondack region of New York is revisited to study the relationship between water chemistry variables associated with acid precipitation and the presence/absence of brook trout (Salvelinus fontinalis) and lake trout (Salvelinus namaycush). For the trout species data sets, water chemistry variables associated with acid precipitation, for example pH and alkalinity, are highly correlated. Regression models to assess their effects on the probability of the presence of fish species are therefore affected by multicollinearity. Because the appropriate regressions are logistic, correction techniques based on least squares do not work. Maximum likelihood parameter estimation is highly unstable for the trout presence/absence data. Developments in weighted multicollinearity diagnostics are used to evaluate maximum likelihood logistic regression parameter estimates. Further, an application of biased parameter estimation is presented as an option to the traditional maximum likelihood logistic regression. Biased estimation methods, like ridge, principal component, or Stein estimation can substantially reduce the variance of the parameter estimates and prediction variance for certain future observations. In many cases, only a slight modification to the converged maximum likelihood estimator is necessary.

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Alheety, Mustafa Ismaeel Naif. "New Versions of Liu-type Estimator in Weighted and non-weighted Mixed Regression Model." Baghdad Science Journal 17, no. 1(Suppl.) (March 18, 2020): 0361. http://dx.doi.org/10.21123/bsj.2020.17.1(suppl.).0361.

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This paper considers and proposes new estimators that depend on the sample and on prior information in the case that they either are equally or are not equally important in the model. The prior information is described as linear stochastic restrictions. We study the properties and the performances of these estimators compared to other common estimators using the mean squared error as a criterion for the goodness of fit. A numerical example and a simulation study are proposed to explain the performance of the estimators.

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Liang, Han-Ying, and Bing-Yi Jing. "Strong Consistency of Estimators for Heteroscedastic Partly Linear Regression Model under Dependent Samples." Journal of Applied Mathematics and Stochastic Analysis 15, no. 3 (January 1, 2002): 207–19. http://dx.doi.org/10.1155/s1048953302000187.

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In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei, 1≤i≤n under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.

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Zhao, Pei Xin. "Quantile Regression for Partially Linear Models with Missing Responses at Random." Applied Mechanics and Materials 727-728 (January 2015): 1013–16. http://dx.doi.org/10.4028/www.scientific.net/amm.727-728.1013.

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In this paper, we propose a weighted quantile regression method for partially linear models with missing response at random. The proposed estimation method can give an efficient estimator for parametric components, and can attenuate the effect of missing responses. Some simulations are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.

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Wang, C. Y., and Hua Yun Chen. "Augmented Inverse Probability Weighted Estimator for Cox Missing Covariate Regression." Biometrics 57, no. 2 (June 2001): 414–19. http://dx.doi.org/10.1111/j.0006-341x.2001.00414.x.

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Alshqaq, Shokrya S., Abdullah A. Ahmadini, and Ali H. Abuzaid. "Some New Robust Estimators for Circular Logistic Regression Model with Applications on Meteorological and Ecological Data." Mathematical Problems in Engineering 2021 (May 25, 2021): 1–15. http://dx.doi.org/10.1155/2021/9944363.

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Maximum likelihood estimation ( MLE ) is often used to estimate the parameters of the circular logistic regression model due to its efficiency under a parametric model. However, evidence has shown that the classical MLE extremely affects the parameter estimation in the presence of outliers. This article discusses the effect of outliers on circular logistic regression and extends four robust estimators, namely, Mallows, Schweppe, Bianco and Yohai estimator BY , and weighted BY estimators, to the circular logistic regression model. These estimators have been successfully used in linear logistic regression models for the same purpose. The four proposed robust estimators are compared with the classical MLE through simulation studies. They demonstrate satisfactory finite sample performance in the presence of misclassified errors and leverage points. Meteorological and ecological datasets are analyzed for illustration.

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Sholiha, Anisatus, Kuzairi Kuzairi, and M. Fariz Fadillah Madianto. "Estimator Deret Fourier Dalam Regresi Nonparametrik dengan Pembobot Untuk Perencanaan Penjualan Camilan Khas Madura." Zeta - Math Journal 4, no. 1 (May 16, 2018): 18–23. http://dx.doi.org/10.31102/zeta.2018.4.1.18-23.

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The purpose of regression analysis is determining the relationship between response variables to predictor variables. To estimate the regression curve there are three approaches, parametric regression, nonparametric regression, and semiparametric regression. In this study, the estimator form of nonparametric regression curve is analyzed by using the Fourier series approach with sine and cosine bases, sine bases, and cosine bases. Based on Weighted Least Square (WLS) optimization, the estimator result can be applied to model the sale planning of Madura typical snacks. Nonparametric regression estimators with the Fourier series approach are weighted with uniform and variance weight. The best model that be obtained in this study for uniform weight, based on cosine and sine basis with GCV value of 1541.015, MSE value of 0.1375912 and determination coefficient value of 0.4728418%. The best model for variance weight is based on cosine and sine basis with a GCV value of 1541.011, MSE value of 0.1375912 and determination coefficient of 0.4728227%.

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Kaido, Hiroaki. "ASYMPTOTICALLY EFFICIENT ESTIMATION OF WEIGHTED AVERAGE DERIVATIVES WITH AN INTERVAL CENSORED VARIABLE." Econometric Theory 33, no. 5 (September 23, 2016): 1218–41. http://dx.doi.org/10.1017/s0266466616000384.

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This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002, Econometrica 70(2), 519–546) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined without any functional-form assumptions. Under general conditions, the identified set is compact and convex and hence admits characterization by its support function. Using this characterization, we derive the semiparametric efficiency bound of the support function when the outcome variable is interval-valued. Using mean regression as an example, we further demonstrate that the support function can be estimated in a regular manner by a computationally simple estimator and that the efficiency bound can be achieved.

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Lendle, Samuel David, Bruce Fireman, and Mark J. van der Laan. "Balancing Score Adjusted Targeted Minimum Loss-based Estimation." Journal of Causal Inference 3, no. 2 (September 1, 2015): 139–55. http://dx.doi.org/10.1515/jci-2012-0012.

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AbstractAdjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment-specific mean with the balancing score property that is additionally locally efficient and doubly robust. We investigate the new estimator’s performance relative to other estimators, including another TMLE, a propensity score matching estimator, an inverse probability of treatment weighted estimator, and a regression-based estimator in simulation studies.

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Newey, Whitney K., and James L. Powell. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions." Econometric Theory 6, no. 3 (September 1990): 295–317. http://dx.doi.org/10.1017/s0266466600005284.

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We consider the linear regression model with censored dependent variable, where the disturbance terms are restricted only to have zero conditional median (or other prespecified quantile) given the regressors and the censoring point. Thus, the functional form of the conditional distribution of the disturbances is unrestricted, permitting heteroskedasticity of unknown form. For this model, a lower bound for the asymptotic covariance matrix for regular estimators of the regression coefficients is derived. This lower bound corresponds to the covariance matrix of an optimally weighted censored least absolute deviations estimator, where the optimal weight is the conditional density at zero of the disturbance. We also show how an estimator that attains this lower bound can be constructed, via nonparametric estimation of the conditional density at zero of the disturbance. As a special case our results apply to the (uncensored) linear model under a conditional median restriction.

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Purhadi, Anita Rahayu, and Gabriella Hillary Wenur. "Geographically Weighted Three-Parameters Bivariate Gamma Regression and Its Application." Symmetry 13, no. 2 (January 26, 2021): 197. http://dx.doi.org/10.3390/sym13020197.

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This study discusses model development for response variables following a bivariate gamma distribution using three-parameters, namely shape, scale and location parameters, paying attention to spatial effects so as to produce different parameter estimator values for each location. This model is called geographically weighted bivariate gamma regression (GWBGR). The method used for parameter estimation is maximum-likelihood estimation (MLE) with the Berndt–Hall–Hall-Hausman (BHHH) algorithm approach. Parameter testing consisted of a simultaneous test using the maximum-likelihood ratio test (MLRT) and a partial test using Wald test. The results of GWBGR modeling three-parameters with fixed weight bisquare kernel showed that the variables that significantly affect the rate of infant mortality (RIM) and rate of maternal mortality (RMM) are the percentage of poor people, the percentage of obstetric complications treated, the percentage of pregnant mothers who received Fe3 and the percentage of first-time pregnant mothers under seventeen years of age. While the percentage of households with clean and healthy lifestyle only significant in several regencies and cities.

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Dong, Hao, and Daniel L. Millimet. "Propensity Score Weighting with Mismeasured Covariates: An Application to Two Financial Literacy Interventions." Journal of Risk and Financial Management 13, no. 11 (November 21, 2020): 290. http://dx.doi.org/10.3390/jrfm13110290.

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Estimation of the causal effect of a binary treatment on outcomes often requires conditioning on covariates to address selection concerning observed variables. This is not straightforward when one or more of the covariates are measured with error. Here, we present a new semi-parametric estimator that addresses this issue. In particular, we focus on inverse propensity score weighting estimators when the propensity score is of an unknown functional form and some covariates are subject to classical measurement error. Our proposed solution involves deconvolution kernel estimators of the propensity score and the regression function weighted by a deconvolution kernel density estimator. Simulations and replication of a study examining the impact of two financial literacy interventions on the business practices of entrepreneurs show our estimator to be valuable to empirical researchers.

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Тихов, Михаил Семенович. "Negative $\lambda$-binomial regression in dose-effect relationship." Herald of Tver State University. Series: Applied Mathematics, no. 4 (December 28, 2022): 53–75. http://dx.doi.org/10.26456/vtpmk649.

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Эта статья посвящена проблеме оценки функции распределения и ее квантилей в зависимости доза-эффект с непараметрической отрицательной $\lambda$-биномиальной регрессией. Здесь предложены ядерные оценки функции распределения, ядро которых взвешивается отрицательной $\lambda$-биномиальной случайной величиной при каждой ковариате. Наши оценки состоятельны, т.е. сходятся к своим оптимальным значениям когда число наблюдений $n$ возрастает до бесконечности. Показано, что эти оценки имеют меньшую асимптотическую дисперсию по сравнению, в частности, с оценками типа Надарая-Ватсона и других оценок. Представлены непараметрические оценки квантилей, полученные путем инвертирования ядерной оценки функции распределения. Асимптотическая нормальность этих оценок с поправкой на смещение сохраняется при некоторых условиях регулярности. В первой части анализируются соотношения между моментами отрицательного $\lambda$-биномиального распределения. Получена новая характеризация распределения Пуассона. This paper is concern to the problem of estimating the distribution function and its quantiles in the dose-effect relationships with nonparametric negative $\lambda$-binomial regression. Here, a kernel-based estimators of the distribution function are proposed, of which kernel is weighted by the negative $\lambda$-binomial random variable at each covariate. Our estimates are consistent, that is, they converge to their optimal values in probability as $n$, the number of observations, grow to infinity. It is shown that these estimates have a smaller asymptotic variance in comparison, in particular, with estimates of the Nadaray-Watson type and other estimates. Nonparametric quantiles estimators obtained by inverting a kernel estimator of the distribution function are offered. It is shown that the asymptotic normality of this bias-adjusted estimator holds under some regularity conditions. In the first part, the relations between the moments of the negative $\lambda$-binomial distribution are analyzed. A new characterization of the Poisson distribution is obtened.

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Schreuder, H. T., Z. Ouyang, and M. Williams. "Point-Poisson, point-pps, and modified point-pps sampling: efficiency and variance estimation." Canadian Journal of Forest Research 22, no. 8 (August 1, 1992): 1071–78. http://dx.doi.org/10.1139/x92-142.

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Modified point-pps (probability proportional to size) sampling selects at least one sample tree per point and yields a fixed sample size. Point-Poisson sampling is as efficient as this modified procedure but less efficient than regular point-pps sampling in a simulation study estimating total volume using either the Horvitz–Thompson (ŶHT) or the weighted regression estimator (Ŷwr). Point-pps sampling is somewhat more efficient than point-Poisson sampling for all estimators except ŶHT, and point-Poisson sampling is always somewhat more efficient than modified point-pps sampling across.all estimators. For board foot volume the regression estimators are more efficient than ŶHT for all three procedures. Point-pps sampling is always most efficient, except for ŶHT, and point-Poisson sampling is always more efficient than the modified point-pps procedure. We recommend using Ŷgr (generalized regression estimator), Ŷwr, or ŶHT for total volume and Ŷgr for board foot volume. Three variance estimators estimate the variances of the regression estimates with small bias; we recommend the simple bootstrap variance estimator because it is simple to compute and does as well as its two main competitors. It does well for ŶHT, too, for all three procedures and should be used for ŶHT in point-Ppisson sampling in preference to the Grosenbaugh variance approximation. An unbiased variance estimator is given for ŶHT with the modified point-pps procedure, but the simple bootstrap variance is equally good.

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Zhang, Dongxue, and Zhiming Xia. "Weighted-averaging estimator for possible threshold in segmented linear regression model." Journal of Statistical Planning and Inference 200 (May 2019): 102–18. http://dx.doi.org/10.1016/j.jspi.2018.09.008.

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Zhang, Rui, Yi Wu, Weifeng Xu, and Xuejun Wang. "On complete consistency for the weighted estimator of nonparametric regression models." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 3 (January 8, 2019): 2319–33. http://dx.doi.org/10.1007/s13398-018-00621-0.

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Liu, Heng, and Xia Cui. "Adaptive estimation for spatially varying coefficient models." AIMS Mathematics 8, no. 6 (2023): 13923–42. http://dx.doi.org/10.3934/math.2023713.

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<abstract><p>In this paper, a new adaptive estimation approach is proposed for the spatially varying coefficient models with unknown error distribution, unlike geographically weighted regression (GWR) and local linear geographically weighted regression (LL), this method can adapt to different error distributions. A generalized Modal EM algorithm is presented to implement the estimation, and the asymptotic property of the estimator is established. Simulation and real data results show that the gain of the new adaptive method over the GWR and LL estimation is considerable for the error of non-Gaussian distributions.</p></abstract>

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Journal articles on the topic 'Weighted regression estimator'

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