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Journal articles on the topic 'Local polynomial kernel estimators'

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Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Hiabu, Munir, María Dolores Martínez-Miranda, Jens Perch Nielsen, Jaap Spreeuw, Carsten Tanggaard, and Andrés M. Villegas. "Global Polynomial Kernel Hazard Estimation." Revista Colombiana de Estadística 38, no. 2 (July 15, 2015): 399–411. http://dx.doi.org/10.15446/rce.v38n2.51668.

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<p>This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail.</p>

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2

Hedger, Richard D., François Martin, Julian J. Dodson, Daniel Hatin, François Caron, and Fred G. Whoriskey. "The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers." ICES Journal of Marine Science 65, no. 7 (June 30, 2008): 1248–59. http://dx.doi.org/10.1093/icesjms/fsn109.

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Abstract Hedger, R. D., Martin, F., Dodson, J, J., Hatin, D., Caron, F., and Whoriskey, F. G. 2008. The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers. – ICES Journal of Marine Science, 65: 1248–1259. The principal method for interpolating the positions and speeds of tagged fish within an array of fixed acoustic receivers is the weighted-mean method, which uses a box-kernel estimator, one of the simplest smoothing options available. This study aimed to determine the relative error of alternative, non-parametric regression methods for estimating these parameters. It was achieved by predicting the positions and speeds of three paths made through a dense array of fixed acoustic receivers within a coastal embayment (Gaspé Bay, Québec, Canada) by a boat with a GPS trailing an ultrasonic transmitter. Transmitter positions and speeds were estimated from the receiver data using kernel estimators, with box and normal kernels and the kernel size determined arbitrarily, and by several non-parametric methods, i.e. a kernel estimator, a smoothing spline, and local polynomial regression, with the kernel size or smoothing span determined by cross-validation. Prediction error of the kernel estimator was highly dependent upon kernel size, and a normal kernel produced less error than the box kernel. Of the methods using cross-validation, local polynomial regression produced least error, suggesting it as the optimal method for interpolation. Prediction error was also strongly dependent on array density. The local polynomial regression method was used to determine the movement patterns of a sample of tagged Atlantic salmon (Salmo salar) smolt and kelt, and American eel (Anguilla rostrata). Analysis of the estimates from local polynomial regression suggested that this was a suitable method for monitoring patterns of fish movement.

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3

Gu, Jingping, Qi Li, and Jui-Chung Yang. "Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution." Econometric Reviews 34, no. 6-10 (December 17, 2014): 979–1010. http://dx.doi.org/10.1080/07474938.2014.956615.

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4

Armstrong, Timothy B., and Michal Kolesár. "Simple and honest confidence intervals in nonparametric regression." Quantitative Economics 11, no. 1 (2020): 1–39. http://dx.doi.org/10.3982/qe1199.

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We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we use critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean‐squared error results in CIs that are nearly efficient and that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n −2/5, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in a Monte Carlo analysis and an empirical application.

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5

Su, Liyun, Tianshun Yan, Yanyong Zhao, and Fenglan Li. "Local Polynomial Regression Solution for Differential Equations with Initial and Boundary Values." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/530932.

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Numerical solutions of the linear differential boundary issues are obtained by using a local polynomial estimator method with kernel smoothing. To achieve this, a combination of a local polynomial-based method and its differential form has been used. The computed results with the use of this technique have been compared with the exact solution and other existing methods to show the required accuracy of it. The effectiveness of this method is verified by three illustrative examples. The presented method is seen to be a very reliable alternative method to some existing techniques for such realistic problems. Numerical results show that the solution of this method is more accurate than that of other methods.

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6

Kong, Efang, and Yingcun Xia. "UNIFORM BAHADUR REPRESENTATION FOR NONPARAMETRIC CENSORED QUANTILE REGRESSION: A REDISTRIBUTION-OF-MASS APPROACH." Econometric Theory 33, no. 1 (February 15, 2016): 242–61. http://dx.doi.org/10.1017/s0266466615000262.

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Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator.

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7

Rahayu, Putri Indi, and Pardomuan Robinson Sihombing. "PENERAPAN REGRESI NONPARAMETRIK KERNEL DAN SPLINE DALAM MEMODELKAN RETURN ON ASSET (ROA) BANK SYARIAH DI INDONESIA." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 14, no. 2 (March 2, 2021): 115. http://dx.doi.org/10.20527/epsilon.v14i2.2968.

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Sharia Bank Return On Assets (ROA) modeling in Indonesia in 2018 aims to analyze the relationship pattern of Retturn On Assets (ROA) with interest rates. The analysis that is often used for modeling is regression analysis. Regression analysis is divided into two, namely parametric and nonparametric. The most commonly used nonparametric regression methods are kernel and spline regression. In this study, the nonparametric regression used was kernel regression with the Nadaraya-Watson (NWE) estimator and Local Polynomial (LPE) estimator, while the spline regression was smoothing spline and B-splines. The fitting curve results show that the best model is the B-splines regression model with a degree of 3 and the number of knots 5. This is because the B-splines regression model has a smooth curve and more closely follows the distribution of data compared to other regression curves. The B-splines regression model has a determination coefficient of R ^ 2 of 74.92%,%, meaning that the amount of variation in the ROA variable described by the B-splines regression model is 74.92%, while the remaining 25.8% is explained by other variables not included in the model.

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8

Cattaneo, Matias D., Michael Jansson, and Xinwei Ma. "Simple Local Polynomial Density Estimators." Journal of the American Statistical Association 115, no. 531 (July 22, 2019): 1449–55. http://dx.doi.org/10.1080/01621459.2019.1635480.

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9

Kikechi, Conlet Biketi, and Richard Onyino Simwa. "On Comparison of Local Polynomial Regression Estimators for P=0 and P=1 in a Model Based Framework." International Journal of Statistics and Probability 7, no. 4 (June 27, 2018): 104. http://dx.doi.org/10.5539/ijsp.v7n4p104.

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This article discusses the local polynomial regression estimator for and the local polynomial regression estimator for in a finite population. The performance criterion exploited in this study focuses on the efficiency of the finite population total estimators. Further, the discussion explores analytical comparisons between the two estimators with respect to asymptotic relative efficiency. In particular, asymptotic properties of the local polynomial regression estimator of finite population total for are derived in a model based framework. The results of the local polynomial regression estimator for are compared with those of the local polynomial regression estimator for studied by Kikechi et al (2018). Variance comparisons are made using the local polynomial regression estimator for and the local polynomial regression estimator for which indicate that the estimators are asymptotically equivalently efficient. Simulation experiments carried out show that the local polynomial regression estimator outperforms the local polynomial regression estimator in the linear, quadratic and bump populations.

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10

Chen, Shouyin, and Na Chen. "Learning by atomic norm regularization with polynomial kernels." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 05 (September 2015): 1550035. http://dx.doi.org/10.1142/s0219691315500356.

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In this paper, we propose a learning scheme for regression generated by atomic norm regularization and data independent hypothesis spaces. The hypothesis spaces based on polynomial kernels are trained from finite datasets, which is independent of the given sample. We also present an error analysis for the proposed atomic norm regularization algorithm with polynomial kernels. When dealing with algorithms with polynomial kernels, the regularization error is a main difficulty. We estimate the regularization error by local polynomial reproduction formula. Better error estimates are derived by applying projection and iteration techniques. Our study shows that the proposed algorithm has a fast convergence rate with O(mζ-1), which is the best convergence rate in the literature.

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11

Dong, Jianping, and Renfang Jiang. "A boundary kernel for local polynomial regression." Communications in Statistics - Theory and Methods 29, no. 7 (January 2000): 1549–58. http://dx.doi.org/10.1080/03610920008832562.

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12

Claeskens, Gerda, and Marc Aerts. "Bootstrapping local polynomial estimators in likelihood-based models." Journal of Statistical Planning and Inference 86, no. 1 (April 2000): 63–80. http://dx.doi.org/10.1016/s0378-3758(99)00154-8.

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13

Sabbah, Camille. "Uniform Confidence Bands for Local Polynomial Quantile Estimators." ESAIM: Probability and Statistics 18 (2014): 265–76. http://dx.doi.org/10.1051/ps/2013035.

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14

Zhao, Peng-Liang. "Asymptotics of kernel estimators based on local maximum likelihood." Journal of Nonparametric Statistics 4, no. 1 (January 1994): 79–90. http://dx.doi.org/10.1080/10485259408832602.

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15

Hall, Peter, and Terence Tao. "Relative efficiencies of kernel and local likelihood density estimators." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64, no. 3 (August 2002): 537–47. http://dx.doi.org/10.1111/1467-9868.00349.

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16

Truong, Young K. "Asymptotic Properties of Kernel Estimators Based on Local Medians." Annals of Statistics 17, no. 2 (June 1989): 606–17. http://dx.doi.org/10.1214/aos/1176347128.

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17

Hagmann, M., and O. Scaillet. "Local multiplicative bias correction for asymmetric kernel density estimators." Journal of Econometrics 141, no. 1 (November 2007): 213–49. http://dx.doi.org/10.1016/j.jeconom.2007.01.018.

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18

Wand, M. P. "A Central Limit Theorem for Local Polynomial Backfitting Estimators." Journal of Multivariate Analysis 70, no. 1 (July 1999): 57–65. http://dx.doi.org/10.1006/jmva.1999.1812.

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19

Cai, Zongwu, Yu Ren, and Linman Sun. "PRICING KERNEL ESTIMATION: A LOCAL ESTIMATING EQUATION APPROACH." Econometric Theory 31, no. 3 (October 27, 2014): 560–80. http://dx.doi.org/10.1017/s0266466614000589.

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This paper investigates a general semiparametric stochastic discount factor formulation that avoids functional form misspecification. A new semiparametric estimation procedure is proposed which combines orthogonality conditions and local linear fitting to give a semiparametric generalized estimating equation approach. Asymptotic properties of the estimators are established and we explore the empirical usefulness of the proposed approach to value-weighted stock returns.

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20

Kim, Minkyoung, Philip Garcia, and Raymond M. Leuthold. "Managing price risks using and local polynomial kernel forecasts." Applied Economics 41, no. 23 (October 2009): 3015–26. http://dx.doi.org/10.1080/00036840701351915.

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21

Härdle, W., and A. Tsybakov. "Local polynomial estimators of the volatility function in nonparametric autoregression." Journal of Econometrics 81, no. 1 (November 1997): 223–42. http://dx.doi.org/10.1016/s0304-4076(97)00044-4.

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22

Li, Yibo, Chao Liu, Senyue Zhang, Wenan Tan, and Yanyan Ding. "Reproducing Polynomial Kernel Extreme Learning Machine." Journal of Advanced Computational Intelligence and Intelligent Informatics 21, no. 5 (September 20, 2017): 795–802. http://dx.doi.org/10.20965/jaciii.2017.p0795.

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Conventional kernel support vector machine (KSVM) has the problem of slow training speed, and single kernel extreme learning machine (KELM) also has some performance limitations, for which this paper proposes a new combined KELM model that build by the polynomial kernel and reproducing kernel on Sobolev Hilbert space. This model combines the advantages of global and local kernel function and has fast training speed. At the same time, an efficient optimization algorithm called cuckoo search algorithm is adopted to avoid blindness and inaccuracy in parameter selection. Experiments were performed on bi-spiral benchmark dataset, Banana dataset, as well as a number of classification and regression datasets from the UCI benchmark repository illustrate the feasibility of the proposed model. It achieves the better robustness and generalization performance when compared to other conventional KELM and KSVM, which demonstrates its effectiveness and usefulness.

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23

Karczewski, Maciej, and Andrzej Michalski. "The study and comparison of one-dimensional kernel estimators – a new approach. Part 1. Theory and methods." ITM Web of Conferences 23 (2018): 00017. http://dx.doi.org/10.1051/itmconf/20182300017.

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In this article we compare and examine the effectiveness of different kernel density estimates for some experimental data. For a given random sample X1, X2, …, Xn we present eight kernel estimators fn of the density function f with the Gaussian kernel and with the kernel given by Epanechnikov [1] using several methods: Silverman’s rule of thumb, the Sheather–Jones method, cross-validation methods, and other better-known plug-in methods [2–5]. To assess the effectiveness of the considered estimators and their similarity, we applied a distance measure for measurable and integrable functions [6]. All numerical calculations were performed for a set of experimental data recording groundwater level at a land reclamation facility (cf. [7–8]). The goal of the paper is to present a method that allows the study of local properties of the examined kernel estimators.

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24

Poměnková, Jitka. "Nonparametric estimate remarks." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 54, no. 3 (2006): 93–100. http://dx.doi.org/10.11118/actaun200654030093.

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Kernel smoothers belong to the most popular nonparametric functional estimates. They provide a simple way of finding structure in data. The idea of the kernel smoothing can be applied to a simple fixed design regression model. This article is focused on kernel smoothing for fixed design regresion model with three types of estimators, the Gasser-Müller estimator, the Nadaraya-Watson estimator and the local linear estimator. At the end of this article figures for ilustration of desribed estimators on simulated and real data sets are shown.

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25

Kiefer, Nicholas M., and Timothy J. Vogelsang. "HETEROSKEDASTICITY-AUTOCORRELATION ROBUST TESTING USING BANDWIDTH EQUAL TO SAMPLE SIZE." Econometric Theory 18, no. 6 (September 24, 2002): 1350–66. http://dx.doi.org/10.1017/s026646660218604x.

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Asymptotic theory for heteroskedasticity autocorrelation consistent (HAC) covariance matrix estimators requires the truncation lag, or bandwidth, to increase more slowly than the sample size. This paper considers an alternative approach covering the case with the asymptotic covariance matrix estimated by kernel methods with truncation lag equal to sample size. Although such estimators are inconsistent, valid tests (asymptotically pivotal) for regression parameters can be constructed. The limiting distributions explicitly capture the truncation lag and choice of kernel. A local asymptotic power analysis shows that the Bartlett kernel delivers the highest power within a group of popular kernels. Finite sample simulations suggest that, regardless of the kernel chosen, the null asymptotic approximation of the new tests is often more accurate than that for conventional HAC estimators and asymptotics. Finite sample results on power show that the new approach is competitive.

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26

Lin, Zhengyan, Degui Li, and Jia Chen. "Change point estimators by local polynomial fits under a dependence assumption." Journal of Multivariate Analysis 99, no. 10 (November 2008): 2339–55. http://dx.doi.org/10.1016/j.jmva.2008.02.036.

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27

Giloni, Avi, and Jeffrey S. Simonoff. "The conditional breakdown properties of least absolute value local polynomial estimators." Journal of Nonparametric Statistics 17, no. 1 (January 2005): 15–30. http://dx.doi.org/10.1080/1048525042000201975.

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28

Suparti, Suparti, and Alan Prahutama. "PEMODELAN REGRESI NONPARAMETRIK MENGGUNAKAN PENDEKATAN POLINOMIAL LOKAL PADA BEBAN LISTRIK DI KOTA SEMARANG." MEDIA STATISTIKA 9, no. 2 (January 24, 2017): 85. http://dx.doi.org/10.14710/medstat.9.2.85-93.

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Semarang is the provincial capital of Central Java, with infrastructure and economic’s growth was high. The phenomenon of power outages that occurred in Semarang, certainly disrupted economic development in Semarang. Large electrical energy consumed by industrial-scale consumers and households in the San Francisco area, monitored or recorded automatically and presented into a historical data load power consumption. Therefore, this study modeling the load power consumption at a time when not influenced by the use of electrical load (t-1)-th. Modeling using nonparametric regression approach with Local polynomial. In this study, the kernel used is a Gaussian kernel. In local polynomial modeling, determined optimum bandwidth. One of the optimum bandwidth determination using the Generalized Cross Validation (GCV). GCV values obtained amounted to 1425.726 with a minimum bandwidth of 394. Modelling generate local polynomial of order 2 with MSE value of 1408.672. Keywords: electrical load, local polinomial, gaussian kernel, GCV.

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29

Cattaneo, Matias D., Michael Jansson, and Xinwei Ma. "Manipulation Testing Based on Density Discontinuity." Stata Journal: Promoting communications on statistics and Stata 18, no. 1 (March 2018): 234–61. http://dx.doi.org/10.1177/1536867x1801800115.

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In this article, we introduce two community-contributed commands, rddensity and rdbwdensity, that implement automatic manipulation tests based on density discontinuity and are constructed using the results for local-polynomial density estimators in Cattaneo, Jansson, and Ma (2017b, Simple local polynomial density estimators, Working paper, University of Michigan). These new tests exhibit better size properties (and more power under additional assumptions) than other conventional approaches currently available in the literature. The first command, rddensity, implements manipulation tests based on a novel local-polynomial density estimation technique that avoids prebinning of the data (improving size properties) and allows for restrictions on other features of the model (improving power properties). The second command, rdbwdensity, implements several bandwidth selectors specifically tailored for the manipulation tests discussed herein. We also provide a companion R package with the same syntax and capabilities as rddensity and rdbwdensity.

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30

Matsui, Kota, Wataru Kumagai, Kenta Kanamori, Mitsuaki Nishikimi, and Takafumi Kanamori. "Variable Selection for Nonparametric Learning with Power Series Kernels." Neural Computation 31, no. 8 (August 2019): 1718–50. http://dx.doi.org/10.1162/neco_a_01212.

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In this letter, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, and (2) approximate the estimator using a few variables by [Formula: see text]-type penalized estimation. We see that the proposed method can be applied to various kernel nonparametric estimation such as kernel ridge regression, kernel-based density, and density-ratio estimation. We prove that the proposed method has the property of variable selection consistency when the power series kernel is used. Here, the power series kernel is a certain class of kernels containing polynomial and exponential kernels. This result is regarded as an extension of the variable selection consistency for the nonnegative garrote (NNG), a special case of the adaptive Lasso, to the kernel-based estimators. Several experiments, including simulation studies and real data applications, show the effectiveness of the proposed method.

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31

Blondin, David. "Rates of strong uniform consistency for local least squares kernel regression estimators." Statistics & Probability Letters 77, no. 14 (August 2007): 1526–34. http://dx.doi.org/10.1016/j.spl.2007.03.037.

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32

Jin, Sainan, Liangjun Su, and Zhijie Xiao. "ADAPTIVE NONPARAMETRIC REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY." Econometric Theory 31, no. 6 (September 8, 2014): 1153–91. http://dx.doi.org/10.1017/s0266466614000450.

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In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton–Raphson estimator and the local profile likelihood estimator are investigated. We show that the proposed estimators are asymptotically equivalent to the infeasible local likelihood estimators [e.g., Aerts and Claeskens (1997) Journal of the American Statistical Association 92, 1536–1545], which require knowledge of the error distribution. Simulation evidence suggests that when the distribution of the error term is different from Gaussian, the adaptive estimators of both conditional mean and variance can often achieve significant efficiency over the conventional local polynomial estimators.

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33

Su, Liyun, and Chenlong Li. "Local Prediction of Chaotic Time Series Based on Polynomial Coefficient Autoregressive Model." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/901807.

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We apply the polynomial function to approximate the functional coefficients of the state-dependent autoregressive model for chaotic time series prediction. We present a novel local nonlinear model called local polynomial coefficient autoregressive prediction (LPP) model based on the phase space reconstruction. The LPP model can effectively fit nonlinear characteristics of chaotic time series with simple structure and have excellent one-step forecasting performance. We have also proposed a kernel LPP (KLPP) model which applies the kernel technique for the LPP model to obtain better multistep forecasting performance. The proposed models are flexible to analyze complex and multivariate nonlinear structures. Both simulated and real data examples are used for illustration.

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34

De Brabanter, K., Y. Liu, and C. Hua. "Convergence rates for uniform confidence intervals based on local polynomial regression estimators." Journal of Nonparametric Statistics 28, no. 1 (November 26, 2015): 31–48. http://dx.doi.org/10.1080/10485252.2015.1113283.

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35

Guerre, Emmanuel, and Camille Sabbah. "UNIFORM BIAS STUDY AND BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATORS OF THE CONDITIONAL QUANTILE FUNCTION." Econometric Theory 28, no. 1 (August 2, 2011): 87–129. http://dx.doi.org/10.1017/s0266466611000132.

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This paper investigates the bias and the weak Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the quantile level, the covariates, and the smoothing parameter. The order of the local polynomial estimator can be higher than the differentiability order of the conditional quantile function. Applications of the results deal with global optimal consistency rates of the local polynomial quantile estimator, performance of random bandwidths, and estimation of the conditional quantile density function. The latter allows us to obtain a simple estimator of the conditional quantile function of the private values in a first-price sealed bids auction under the independent private values paradigm and risk neutrality.

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36

Wang, Qifeng, Xiaolin Hu, Xiaobao Deng, and Nicholas E. Buris. "DoA Estimation Using Neural Tangent Kernel under Electromagnetic Mutual Coupling." Electronics 10, no. 9 (April 29, 2021): 1057. http://dx.doi.org/10.3390/electronics10091057.

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Antenna element mutual coupling degrades the performance of Direction of Arrival (DoA) estimation significantly. In this paper, a novel machine learning-based method via Neural Tangent Kernel (NTK) is employed to address the DoA estimation problem under the effect of electromagnetic mutual coupling. NTK originates from Deep Neural Network (DNN) considerations, based on the limiting case of an infinite number of neurons in each layer, which ultimately leads to very efficient estimators. With the help of the Polynomial Root Finding (PRF) technique, an advanced method, NTK-PRF, is proposed. The method adapts well to multiple-signal scenarios when sources are far apart. Numerical simulations are carried out to demonstrate that this NTK-PRF approach can handle, accurately and very efficiently, multiple-signal DoA estimation problems with realistic mutual coupling.

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37

Kong, Efang, Oliver Linton, and Yingcun Xia. "UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL." Econometric Theory 26, no. 5 (March 5, 2010): 1529–64. http://dx.doi.org/10.1017/s0266466609990661.

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We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi,Xi)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model.

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38

Bolbolian Ghalibaf, Mohammad. "Kernel Function in Local Linear Peters-Belson Regression." Revista Colombiana de Estadística 41, no. 2 (July 1, 2018): 235–49. http://dx.doi.org/10.15446/rce.v41n2.65654.

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Determining the extent of a disparity, if any, between groups of people, for example, race or gender, is of interest in many fields, including public health for medical treatment and prevention of disease or in discrimination cases concerning equal pay to estimate the pay disparities between minority and majority employees. An observed difference in the mean outcome between a majority/advantaged group (AG) and minority/disadvantaged group (DG) can be due to differences in the distribution of relevant covariates. The Peters Belson (PB) method fits a regression model with covariates to the AG to predict, for each DG member, their outcome measure as if they had been from the AG. The difference between the mean predicted and the mean observed outcomes of DG members is the (unexplained) disparity of interest. PB regression is a form of statistical matching, akin in spirit to Bhattacharya's band-width matching. In this paper we review the use of PB regression in legal cases from Hikawa et al. (2010b) Parametric and nonparametric approaches to PB regression are described and we show that in nonparametric PB regression choose a kernel function can be better resulted, i.e. by selecting the appropriate kernel function we can reduce bias and variance of estimators, also increase power of test.

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39

Bouezmarni, T., A. El Ghouch, and M. Mesfioui. "Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data." Journal of Probability and Statistics 2011 (2011): 1–16. http://dx.doi.org/10.1155/2011/937574.

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The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations.

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Fan, Jianqing, Nancy E. Heckman, and M. P. Wand. "Local Polynomial Kernel Regression for Generalized Linear Models and Quasi-Likelihood Functions." Journal of the American Statistical Association 90, no. 429 (March 1995): 141–50. http://dx.doi.org/10.1080/01621459.1995.10476496.

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Perron, Pierre, and Serena Ng. "AN AUTOREGRESSIVE SPECTRAL DENSITY ESTIMATOR AT FREQUENCY ZERO FOR NONSTATIONARITY TESTS." Econometric Theory 14, no. 5 (October 1998): 560–603. http://dx.doi.org/10.1017/s0266466698145024.

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Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant increase in the bias and mean-squared error (MSE) of kernel-based estimators. We then consider a variant of the autoregressive spectral density estimator that does not share these shortcomings because it bypasses the use of the estimate from the AR(1) regression. Simulations and local asymptotic analyses show its bias and MSE to be much smaller than those of a kernel-based estimator when there is strong negative serial correlation. We also include a discussion about the appropriate choice of the truncation lag.

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CHEN, FENG, PAUL S. F. YIP, and K. F. LAM. "On the Local Polynomial Estimators of the Counting Process Intensity Function and its Derivatives." Scandinavian Journal of Statistics 38, no. 4 (May 13, 2011): 631–49. http://dx.doi.org/10.1111/j.1467-9469.2011.00733.x.

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Wu, Chengmao, and Zeren Wang. "A robust kernel-based fuzzy local neighborhood clustering with quadratic polynomial-center clusters." Digital Signal Processing 118 (November 2021): 103200. http://dx.doi.org/10.1016/j.dsp.2021.103200.

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De Giosa, Marcello, and Rosa Maria Mininni. "Free area estimation in a partially observed dynamic germ-grain model." Journal of Applied Mathematics and Stochastic Analysis 15, no. 4 (January 1, 2002): 287–307. http://dx.doi.org/10.1155/s1048953302000254.

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The estimation problem of the expected local fraction of free area function S for a partially observed dynamic germ-grain model is presented. Properties of the estimators are proved by martingale and product integral methods. Confidence bounds are provided. Furthermore, an estimator of the hazard rate α(t)=−dS(t)/(S(t)dt) is obtained by the kernel function method and asymptotic properties of the estimator are proved and used to find confidence intervals. By a simulated illustrative example, the qualitative behavior of the estimators is shown.

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Ghauch, Ziad Georges. "Efficient polynomial chaos approximations: Active, local and basis-adapted." ANZIAM Journal 62 (June 8, 2021): C16—C29. http://dx.doi.org/10.21914/anziamj.v62.15833.

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Metamodels provide an efficient means for the approximation of response surfaces of systems, particularly for resource-intensive experiment designs. It is oftentimes the case that interest is focused on a specific region of the parameter space. We propose an efficient recipe for the local approximation of response surfaces using Polynomial Chaos techniques. For systems embedded in high-dimensional settings, a basis-adapted spectral representation is exploited locally for dimension reduction. The proposed approach comprises an initial heuristic global solution for parameter space exploration using an approximate global Polynomial Chaos metamodel, followed by a local design being refined through an active learning scheme. The problem of turbulent flow around a symmetric airfoil is considered. Statistical estimators based on the local, active, basis-adapted approach show less bias and faster convergence as compared to the estimators from a global solution. References B. J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. McFarland. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J. 46(10):2459–2468, 2008. doi: 10.2514/1.34321. G. E. P. Box and N. R. Draper. Empirical Model-Building and Response Surfaces. Wiley, 1987. V. Dubourg, B. Sudret, and F. Deheeger. Metamodel-based importance sampling for structural reliability analysis. Prob. Eng. Mech. 33:47–57, 2013. doi: 10.1016/j.probengmech.2013.02.002. R. G. Ghanem and P. D. Spanos. Stochastic finite element: A spectral approach. Dover, 1991. doi: 10.1007/978-1-4612-3094-6. Z. G. Ghauch. Leveraging adapted polynomial chaos metamodels for real-time Bayesian updating. J. Verif. Valid. Uncert. 4(4):041003, 2020. doi: 10.1115/1.4045693. Z. G. Ghauch, V. Aitharaju, W. R. Rodgers, P. Pasupuleti, A. Dereims, and R. G. Ghanem. Integrated stochastic analysis of fiber composites manufacturing using adapted polynomial chaos expansions. Compos. Part A: Appl. Sci. 118:179–193, 2019. doi: 10.1016/j.compositesa.2018.12.029. M. E. Johnson, L. M. Moore, and D. Ylvisaker. Minimax and maximin distance designs. J. Stat. Plan. Infer. 26(2):131–148, 1990. doi: 10.1016/0378-3758(90)90122-B. A. Notin, N. Gayton, J. L. Dulong, M. Lemaire, P. Villon, and H. Jaffal. RPCM: A strategy to perform reliability analysis using polynomial chaos and resampling. Euro. J. Comput. Mech. 19(8):795–830, 2010. doi: 10.3166/ejcm.19.795-830. OpenCFD. OpenFOAM User’s Guide. 2019. https://www.openfoam.com/documentation/user-guide. V. Picheny, D. Ginsbourger, O. Roustant, R. T Haftka, and N.-H. Kim. Adaptive designs of experiments for accurate approximation of target regions. J. Mech. Design. 132(7):071008, 2010. doi: 10.1115/1.4001873. C. Thimmisetty, P. Tsilifis, and R. Ghanem. Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem. AI EDAM 31(3):265–276, 2017. doi: 10.1017/S0890060417000166. R. Tipireddy and R. Ghanem. Basis adaptation in homogeneous chaos spaces. J. Comput. Phys. 259:304–317, 2014. doi: 10.1016/j.jcp.2013.12.009. P. Tsilifis and R. G. Ghanem. Reduced Wiener chaos representation of random fields via basis adaptation and projection. J. Comput. Phys. 341:102–120, 2017. doi: 10.1016/j.jcp.2017.04.009. Turbulence Modeling Resource. NASA Langley Research Center. Washington, DC, 2018. http://turbmodels.larc.nasa.gov/.

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Leonardo, Leonardo, Yohannes Yohannes, and Ery Hartati. "Klasifikasi Sampah Daur Ulang Menggunakan Support Vector Machine Dengan Fitur Local Binary Pattern." Jurnal Algoritme 1, no. 1 (October 10, 2020): 78–90. http://dx.doi.org/10.35957/algoritme.v1i1.440.

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Garbage is one of the problems that always arise in Indonesia and even in the world. Increasingly, the production of waste is increased along with the increase in population and consumption. Therefore, need a prevention to stop wasting or producing garbage through recycle. This research do garbage recycle classification of cardboard, glass, metal, paper and plastic by using Local Binary Pattern (LBP) texture feature extraction methode and Support Vector Machine (SVM) as classification methode. For examination technic and dataset distribution is using K-Fold Cross Validation methode type Leave One Out (LOO). From examination result had been done were using fold 5 until fold 10. Polynomial kernel get highest accuracy result from every fold used with mean point 87.82%. Based on SVM classification examination result whether linear kernel, polynomial nor gaussian by using fold 5 until fold 10. The best accuracy point for cardboard garbage is 96.01%. For glass garbage, the best accuracy point is 90.62%. Then, metal garbage get the best accuracy point 89.72%. While paper garbage with highest accuracy point 96.01%. And plastic garbage with highest accuracy point 87.64%.

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Ziegelmann, Flavio A. "NONPARAMETRIC ESTIMATION OF VOLATILITY FUNCTIONS: THE LOCAL EXPONENTIAL ESTIMATOR." Econometric Theory 18, no. 4 (May 17, 2002): 985–91. http://dx.doi.org/10.1017/s026646660218409x.

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Kernel smoothing techniques free the traditional parametric estimators of volatility from the constraints related to their specific models. In this paper the nonparametric local exponential estimator is applied to estimate conditional volatility functions, ensuring its nonnegativity. Its asymptotic properties are established and compared with those for the local linear estimator. It theoretically enables us to determine when the exponential is expected to be superior to the linear estimator. A very strong and novel result is achieved: the exponential estimator is asymptotically fully adaptive to unknown conditional mean functions. Also, our simulation study shows superior performance of the exponential estimator.

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Kauermann, Göran, Marlene Müller, and Raymond J. Carroll. "The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations." Statistics & Probability Letters 37, no. 1 (January 1998): 41–47. http://dx.doi.org/10.1016/s0167-7152(97)00098-9.

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Aerts, Marc, Ilse Augustyns, and Paul Janssen. "Central limit theorem for the total squared error of local polynomial estimators of cell probabilities." Journal of Statistical Planning and Inference 91, no. 2 (December 2000): 181–93. http://dx.doi.org/10.1016/s0378-3758(00)00177-4.

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Tenreiro, Carlos. "Asymptotic normality of local polynomial estimators of regression function and its derivatives for time series." Journal of Nonparametric Statistics 8, no. 4 (January 1997): 365–78. http://dx.doi.org/10.1080/10485259708832731.

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