Journal articles: 'Non-Asymptotic and robust estimation'

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Hirose, Kei, and Hiroki Masuda. "Robust Relative Error Estimation." Entropy 20, no. 9 (August 24, 2018): 632. http://dx.doi.org/10.3390/e20090632.

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Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the γ -likelihood function, which is constructed through γ -cross entropy with keeping the original statistical model in use. The estimating equation has a redescending property, a desirable property in robust statistics, for a broad class of noise distributions. To find a minimizer of the negative γ -likelihood function, a majorize-minimization (MM) algorithm is constructed. The proposed algorithm is guaranteed to decrease the negative γ -likelihood function at each iteration. We also derive asymptotic normality of the corresponding estimator together with a simple consistent estimator of the asymptotic covariance matrix, so that we can readily construct approximate confidence sets. Monte Carlo simulation is conducted to investigate the effectiveness of the proposed procedure. Real data analysis illustrates the usefulness of our proposed procedure.

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Rudenko, O. G., О. О. Bessonov, N. М. Serdyuk, К. О. Olijnik, and О. S. Romanyuk. "Robust object identification in the presence of non-Gaussian interference." Bionics of Intelligence 2, no. 93 (December 2, 2019): 7–12. http://dx.doi.org/10.30837/bi.2019.2(93).02.

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The problem of identifying the parameters of a linear object in the presence of non-Gaussian interference is considered based on minimizing a combined functional that combines the properties of OLS and IIS. The conditions for the convergence of the gradient identification algorithm in mean and mean square are determined. Analytical estimates are obtained for non-asymptotic and asymptotic values of the parameter estimation error and the identification accuracy. It is shown that these values of the estimation error and identification accuracy depend on the choice of the mixing parameter.

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Ekundayo, Gbenga, and Ndubuisi Jeffery Jamani. "Estimation of Audit Delay Determinants: Do Outliers and Asymptotic Properties Matter?" European Journal of Business and Management Research 7, no. 5 (September 26, 2022): 54–62. http://dx.doi.org/10.24018/ejbmr.2022.7.5.1604.

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The overriding objective of the study is to empirically examine if outliers and asymptotic properties of estimators matter in the estimation of audit delay determinants. The study employed the ex-post causal research design and focuses on a sample of ten (10) listed oil and gas firms in Nigeria. Secondary data from the content analysis of annual reports spanning the period 2010-2019 was used for the study. The study investigates if outliers and asymptotic properties matter in estimation outcomes comparing the following estimators; the standard OLS, Bootstrapped OLS and Robust estimators. The outcome of the study revealed that the robust estimator yields results that are significantly different from those of both the OLS and Bootstrapped OLS estimations. This suggests that the failure to address outliers in standard OLS estimations can significantly bias the estimation outcome and may be responsible for the myriad of inconclusive outcomes observed in the extant academic literature. Hence, the study confirms that in the estimation of determinants of audit delay, the considerations of outliers indeed constitute a significant statistical consideration for researchers and even more germane than asymptotic concerns.

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Calderon, Sergio, and Daniel Ordoñez Callamad. "Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study." Revista Colombiana de Estadística 45, no. 1 (January 1, 2022): 1–39. http://dx.doi.org/10.15446/rce.v45n1.92965.

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The effect of additive outliers is studied on an adapted non-linearity test and a robust estimation method for autoregressive coefficients in open-loop TAR (threshold autoregressive) models. Through a Monte Carlo experiment, the power and size of the non-linearity test are studied. Regarding the estimation method, the bias and ratio of mean squared errors are compared between the robust estimator and least squares. Simulation exercises are carried out for different percentages of contamination and the proportion of observations on each model regime. Furthermore, the approximation of the univariate normal distribution to the empirical distribution of estimated coefficients is analyzed along with the coverage level of asymptotic confidence intervals for the parameters. Results show that the adapted non-linearity test does not have size distortions, and it has a superior power than its least-squares counterpart when additive outliers are present. On the other hand, the robust estimation method for the autoregressive coefficients has a better mean squared error than least-squares when this type of observations are present. Lastly, the use of the non-linearity test and the estimation method are illustrated through a real example.

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Liu, Jie, Da-Yan Liu, Driss Boutat, Xuefeng Zhang, and Ze-Hao Wu. "Innovative non-asymptotic and robust estimation method using auxiliary modulating dynamical systems." Automatica 152 (June 2023): 110953. http://dx.doi.org/10.1016/j.automatica.2023.110953.

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Fiteni, Inmaculada. "ROBUST ESTIMATION OF STRUCTURAL BREAK POINTS." Econometric Theory 18, no. 2 (April 2002): 349–86. http://dx.doi.org/10.1017/s0266466602182065.

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This paper proposes robust M-estimators of dynamic linear models with a structural break of unknown location. Rates of convergence and limiting distributions for the estimated shift point and the estimated regression parameters are derived. The analysis is carried out in the framework of possibly dependent observations and also with trending regressors. The asymptotic distribution of the break location estimator is obtained both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases. The latter is essential for the derivation of feasible confidence intervals for the break location. Monte Carlo simulations illustrate the performance of asymptotic inferences in practice.

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Ritov, Ya'acov. "Asymptotic results in robust quasi-bayesian estimation." Journal of Multivariate Analysis 23, no. 2 (December 1987): 290–302. http://dx.doi.org/10.1016/0047-259x(87)90158-8.

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Poudyal, Chudamani. "ROBUST ESTIMATION OF LOSS MODELS FOR LOGNORMAL INSURANCE PAYMENT SEVERITY DATA." ASTIN Bulletin 51, no. 2 (March 5, 2021): 475–507. http://dx.doi.org/10.1017/asb.2021.4.

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AbstractThe primary objective of this scholarly work is to develop two estimation procedures – maximum likelihood estimator (MLE) and method of trimmed moments (MTM) – for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.

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Vermeulen, Karel, and Stijn Vansteelandt. "Data-Adaptive Bias-Reduced Doubly Robust Estimation." International Journal of Biostatistics 12, no. 1 (May 1, 2016): 253–82. http://dx.doi.org/10.1515/ijb-2015-0029.

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Abstract Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

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Chen, Haiqiang. "ROBUST ESTIMATION AND INFERENCE FOR THRESHOLD MODELS WITH INTEGRATED REGRESSORS." Econometric Theory 31, no. 4 (October 27, 2014): 778–810. http://dx.doi.org/10.1017/s0266466614000553.

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This paper studies the robust estimation and inference of threshold models with integrated regressors. We derive the asymptotic distribution of the profiled least squares (LS) estimator under the diminishing threshold effect assumption that the size of the threshold effect converges to zero. Depending on how rapidly this sequence converges, the model may be identified or only weakly identified and asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a model-selection procedure is applied to determine the model identification strength and to construct robust confidence intervals, which have the correct asymptotic size irrespective of the magnitude of the threshold effect. The model is then generalized to incorporate endogeneity and serial correlation in error terms, under which, we design a Cochrane–Orcutt feasible generalized least squares (FGLS) estimator which enjoys efficiency gains and robustness against different error specifications, including both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to test for the existence of the threshold effect. Monte Carlo simulations show that our estimators and test statistics perform well.

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Qu, Zhihua, Darren M. Dawson, John F. Dorsey, and John D. Duffie. "Robust estimation and control of robotic manipulators." Robotica 13, no. 3 (May 1995): 223–31. http://dx.doi.org/10.1017/s0263574700017756.

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SummaryFor the trajectory following problem of a robot manipulator, a robust estimation and control scheme which requires only position measurements is proposed to guarantee uniform ultimate bounded stability under significant uncertainties and disturbances in the robot dynamics. The scheme combines a class of robust control laws with a robust estimator where the robust control law can be chosen to be either a modification of the standard computed torque control law or simply a linear and decentralized “PD” control law. The proposed robust estimator is also linear and decentralized for easy implementation. Constructive choices of the gains in the control law and estimator are proposed which depend only on the coefficients of a polynomial bounding function of the unknown dynamics. The asymptotic stability of the tracking errors and the estimation error is also investigated. Experimentation results verify the theoretical analysis.

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Cao, Shiyun, and Qiankun Zhou. "Common Correlated Effects Estimation for Dynamic Heterogeneous Panels with Non-Stationary Multi-Factor Error Structures." Econometrics 10, no. 3 (August 11, 2022): 29. http://dx.doi.org/10.3390/econometrics10030029.

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In this paper, we consider the estimation of a dynamic panel data model with non-stationary multi-factor error structures. We adopted the common correlated effect (CCE) estimation and established the asymptotic properties of the CCE and common correlated effects mean group (CCEMG) estimators, as N and T tend to infinity. The results show that both the CCE and CCEMG estimators are consistent and the CCEMG estimator is asymptotically normally distributed. The theoretical findings were supported for small samples by an extensive simulation study, showing that the CCE estimators are robust to a wide variety of data generation processes. Empirical findings suggest that the CCE estimation is widely applicable to models with non-stationary factors. The proposed procedure is also illustrated by an empirical application to analyze the U.S. cigar dataset.

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Kunitomo, Naoto, Naoki Awaya, and Daisuke Kurisu. "Comparing estimation methods of non-stationary errors-in-variables models." Japanese Journal of Statistics and Data Science 3, no. 1 (June 15, 2019): 73–101. http://dx.doi.org/10.1007/s42081-019-00051-1.

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AbstractWe investigate the estimation methods of the multivariate non-stationary errors-in-variables models when there are non-stationary trend components and the measurement errors or noise components. We compare the maximum likelihood (ML) estimation and the separating information maximum likelihood (SIML) estimation. The latter was proposed by Kunitomo and Sato (Trend, seasonality and economic time series: the nonstationary errors-in-variables models. MIMS-RBP-SDS-3, MIMS, Meiji University. http://www.mims.meiji.ac.jp/, 2017) and Kunitomo et al. (Separating information maximum likelihood method for high-frequency financial data. Springer, Berlin, 2018). We have found that the Gaussian likelihood function can have non-concave shape in some cases and the ML method does work only when the Gaussianity of non-stationary and stationary components holds with some restrictions such as the signal–noise variance ratio in the parameter space. The SIML estimation has the asymptotic robust properties in more general situations. We explore the finite sample and asymptotic properties of the ML and SIML methods for the non-stationary errors-in variables models.

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Holst, Klaus Kähler, and Esben Budtz-Jørgensen. "A two-stage estimation procedure for non-linear structural equation models." Biostatistics 21, no. 4 (January 29, 2019): 676–91. http://dx.doi.org/10.1093/biostatistics/kxy082.

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Summary Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. In this article, we introduce a simple two-stage estimation technique for estimation of non-linear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the non-linear effect are predicted by their conditional means. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modeled using restricted cubic splines, and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to MLE and alternative two-stage estimation techniques.

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Coffman, Donna L., Alberto Maydeu-Olivares, and Jaume Arnau. "Asymptotic Distribution Free Interval Estimation." Methodology 4, no. 1 (January 2008): 4–9. http://dx.doi.org/10.1027/1614-2241.4.1.4.

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Abstract. Confidence intervals for the intraclass correlation coefficient (ICC) have been proposed under the assumption of multivariate normality. We propose confidence intervals which do not require distributional assumptions. We performed a simulation study to assess the coverage rates of normal theory (NT) and asymptotically distribution free (ADF) intervals. We found that the ADF intervals performed better than the NT intervals when kurtosis was greater than 4. When violations of distributional assumptions were not too severe, both the intervals performed about the same. The point estimate of the ICC was robust to distributional violations. We provide R code for computing the ADF confidence intervals for the ICC.

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Chernozhukov, Victor, Juan Carlos Escanciano, Hidehiko Ichimura, Whitney K. Newey, and James M. Robins. "Locally Robust Semiparametric Estimation." Econometrica 90, no. 4 (2022): 1501–35. http://dx.doi.org/10.3982/ecta16294.

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Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross‐fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

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Čížek, Pavel. "GENERAL TRIMMED ESTIMATION: ROBUST APPROACH TO NONLINEAR AND LIMITED DEPENDENT VARIABLE MODELS." Econometric Theory 24, no. 6 (July 9, 2008): 1500–1529. http://dx.doi.org/10.1017/s0266466608080596.

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High-breakdown-point regression estimators protect against large errors and data contamination. We generalize the concept of trimming used by many of these robust estimators, such as the least trimmed squares and maximum trimmed likelihood, and propose a general trimmed estimator, which renders robust estimators applicable far beyond the standard (non)linear regression models. We derive here the consistency and asymptotic distribution of the proposed general trimmed estimator under mild β-mixing conditions and demonstrate its applicability in nonlinear regression and limited dependent variable models.

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Sánchez Torres, Juan Diego, Héctor A. Botero, Esteban Jiménez, Oscar Jaramillo, and Alexander G. Loukianov. "A Robust Extended State Observer for the Estimation of Concentration and Kinetics in a CSTR." International Journal of Chemical Reactor Engineering 14, no. 1 (February 1, 2016): 481–90. http://dx.doi.org/10.1515/ijcre-2015-0149.

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AbstractThis paper presents a state estimation structure for a Continuous Stirred Tank Reactor (CSTR), by means of an Asymptotic Observer jointly with a disturbance high order sliding mode-based estimator. The proposed estimation scheme allows the asymptotic reconstruction of the concentration inside the reactor based on the measures of the temperature inside the reactor and the temperature inside the jacket, in presence of changes in the global coefficient of heat transfer $UA$, the Arrhenius constant ${k_0}$ and the activation energy E. Additionally, the structure is able to estimate $UA$ and the kinetics term ${k_0}{e^{- {E \over {RT}}}}$. The properties of the proposed scheme are proved mathematically and verified through numerical simulations.

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Machado, José A. F. "Robust Model Selection and M-Estimation." Econometric Theory 9, no. 3 (June 1993): 478–93. http://dx.doi.org/10.1017/s0266466600007775.

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This paper studies the qualitative robustness properties of the Schwarz information criterion (SIC) based on objective functions defining M-estimators. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness in model selection is the uniform boundedness of the objective function. In the process, the asymptotic performance of the SIC for general M-estimators is also studied. The paper concludes with a Monte Carlo study of the finite sample behavior of the SIC for different specifications of the sample objective function.

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Srivastava, Manoj Kumar, and Namita Srivastava. "Robust estimation of finite population total." Statistics in Transition new series 11, no. 1 (July 16, 2010): 127–44. http://dx.doi.org/10.59170/stattrans-2010-008.

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The present paper deals with the robust prediction of finite population total under the superpopulation modelGR. The design is de-emphasized while developing these predictors under the superpopulation model and making comparison among all resistant estimators. The suggested proposals involve reweighed iterative algorithm for Robust Prediction. The discussion also involves the calculation of asymptotic bias and variance in terms of the influence function computed for these predictors. Two populations have been considered for simulation study to judge the performance of proposed predictors with conventional and model based existing alternatives.

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Cai, T. Tony, and Harrison H. Zhou. "Asymptotic equivalence and adaptive estimation for robust nonparametric regression." Annals of Statistics 37, no. 6A (December 2009): 3204–35. http://dx.doi.org/10.1214/08-aos681.

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Castilla, Elena, and Abhik Ghosh. "Robust Minimum Divergence Estimation for the Multinomial Circular Logistic Regression Model." Entropy 25, no. 10 (October 7, 2023): 1422. http://dx.doi.org/10.3390/e25101422.

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Circular data are extremely important in many different contexts of natural and social science, from forestry to sociology, among many others. Since the usual inference procedures based on the maximum likelihood principle are known to be extremely non-robust in the presence of possible data contamination, in this paper, we develop robust estimators for the general class of multinomial circular logistic regression models involving multiple circular covariates. Particularly, we extend the popular density-power-divergence-based estimation approach for this particular set-up and study the asymptotic properties of the resulting estimators. The robustness of the proposed estimators is illustrated through extensive simulation studies and few important real data examples from forest science and meteorology.

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Youssef, Ahmed H., Mohamed R. Abonazel, and Amr R. Kamel. "Efficiency Comparisons of Robust and Non-Robust Estimators for Seemingly Unrelated Regressions Model." WSEAS TRANSACTIONS ON MATHEMATICS 21 (May 6, 2022): 218–44. http://dx.doi.org/10.37394/23206.2022.21.28.

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This paper studies and reviews several procedures for developing robust regression estimators of the seemingly unrelated regressions (SUR) model, when the variables are affected by outliers. To compare the robust estimators (M-estimation, S-estimation, and MM-estimation) with non-robust (traditional maximum likelihood and feasible generalized least squares) estimators of this model with outliers, the Monte Carlo simulation study has been performed. The simulation factors of our study are the number of equations in the system, the number of observations, the contemporaneous correlation among equations, the number of regression parameters, and the percentages of outliers in the dataset. The simulation results showed that, based on total mean squared error (TMSE), total mean absolute error (TMAE) and relative absolute bias (RAB) criteria, robust estimators give better performance than non-robust estimators; specifically, the MM-estimator is more efficient than other estimators. While when the dataset does not contain outliers, the results showed that the unbiased SUR estimator (feasible generalized least squares estimator) is more efficient than other estimators.

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Yamada, Makoto, Taiji Suzuki, Takafumi Kanamori, Hirotaka Hachiya, and Masashi Sugiyama. "Relative Density-Ratio Estimation for Robust Distribution Comparison." Neural Computation 25, no. 5 (May 2013): 1324–70. http://dx.doi.org/10.1162/neco_a_00442.

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Divergence estimators based on direct approximation of density ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution comparison such as outlier detection, transfer learning, and two-sample homogeneity test. However, since density-ratio functions often possess high fluctuation, divergence estimation is a challenging task in practice. In this letter, we use relative divergences for distribution comparison, which involves approximation of relative density ratios. Since relative density ratios are always smoother than corresponding ordinary density ratios, our proposed method is favorable in terms of nonparametric convergence speed. Furthermore, we show that the proposed divergence estimator has asymptotic variance independent of the model complexity under a parametric setup, implying that the proposed estimator hardly overfits even with complex models. Through experiments, we demonstrate the usefulness of the proposedapproach.

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Shergei, M., U. Shaked, and C. E. De Souza. "Robust ℋ∞ non-linear estimation." International Journal of Adaptive Control and Signal Processing 10, no. 4-5 (July 1996): 395–408. http://dx.doi.org/10.1002/(sici)1099-1115(199607)10:4/5<395::aid-acs370>3.0.co;2-n.

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BIAN, GUORUI, MICHAEL McALEER, and WING-KEUNG WONG. "ROBUST ESTIMATION AND FORECASTING OF THE CAPITAL ASSET PRICING MODEL." Annals of Financial Economics 08, no. 02 (December 2013): 1350007. http://dx.doi.org/10.1142/s2010495213500073.

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In this paper, we develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution. We obtain the closed form of the estimators, derive the asymptotic properties, and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model (CAPM) by comparing its performance with least squares estimators (LSE) on the monthly returns of US portfolios. The empirical results reveal that the MML estimators are more efficient than LSE in terms of the relative efficiency of one-step-ahead forecast mean square error in small samples.

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Chang, Chaojie. "Research on Two-stage Estimation of Partially Linear Single-index Model with Longitudinal Data." Academic Journal of Science and Technology 5, no. 1 (February 28, 2023): 112–15. http://dx.doi.org/10.54097/ajst.v5i1.5438.

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Partial linear single-index model is a kind of semi-parametric model with wide application. In this paper, we deal with the partial linear single-index model under longitudinal data. A "two-stage estimation method" without iteration by using local polynomial and bias correction generalized estimation equation is proposed. under some regularity conditions, the asymptotic properties of the connection function and unknown parameter estimator are investigated. Numerical simulation shows that the proposed method is robust.

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Zhou, Xingcai, and Fangxia Zhu. "Wavelet-M-Estimation for Time-Varying Coefficient Time Series Models." Discrete Dynamics in Nature and Society 2020 (September 3, 2020): 1–11. http://dx.doi.org/10.1155/2020/1025452.

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This paper proposes wavelet-M-estimation for time-varying coefficient time series models by using a robust-type wavelet technique, which can adapt to local features of the time-varying coefficients and does not require the smoothness of the unknown time-varying coefficient. The wavelet-M-estimation has the desired asymptotic properties and can be used to estimate conditional quantile and to robustify the usual mean regression. Under mild assumptions, the Bahadur representation and the asymptotic normality of wavelet-M-estimation are established.

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Wang, Andong, Guoxu Zhou, and Qibin Zhao. "Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data." Remote Sensing 13, no. 18 (September 14, 2021): 3671. http://dx.doi.org/10.3390/rs13183671.

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This paper conducts a rigorous analysis for the problem of robust tensor completion, which aims at recovering an unknown three-way tensor from incomplete observations corrupted by gross sparse outliers and small dense noises simultaneously due to various reasons such as sensor dead pixels, communication loss, electromagnetic interferences, cloud shadows, etc. To estimate the underlying tensor, a new penalized least squares estimator is first formulated by exploiting the low rankness of the signal tensor within the framework of tensor ∗L-Singular Value Decomposition (∗L-SVD) and leveraging the sparse structure of the outlier tensor. Then, an algorithm based on the Alternating Direction Method of Multipliers (ADMM) is designed to compute the estimator in an efficient way. Statistically, the non-asymptotic upper bound on the estimation error is established and further proved to be optimal (up to a log factor) in a minimax sense. Simulation studies on synthetic data demonstrate that the proposed error bound can predict the scaling behavior of the estimation error with problem parameters (i.e., tubal rank of the underlying tensor, sparsity of the outliers, and the number of uncorrupted observations). Both the effectiveness and efficiency of the proposed algorithm are evaluated through experiments for robust completion on seven different types of remote sensing data.

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Cavaliere, Giuseppe, and Iliyan Georgiev. "ROBUST INFERENCE IN AUTOREGRESSIONS WITH MULTIPLE OUTLIERS." Econometric Theory 25, no. 6 (December 2009): 1625–61. http://dx.doi.org/10.1017/s0266466609990272.

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We consider robust methods for estimation and unit root (UR) testing in autoregressions with infrequent outliers whose number, size, and location can be random and unknown. We show that in this setting standard inference based on ordinary least squares estimation of an augumented Dickey–Fuller (ADF) regression may not be reliable, because (a) clusters of outliers may lead to inconsistent estimation of the autoregressive parameters and (b) large outliers induce a jump component in the asymptotic distribution of UR test statistics. In the benchmark case of known outlier location, we discuss why the augmentation of the ADF regression with appropriate dummy variables not only ensures consistent parameter estimation but also gives rise to UR tests with significant power gains, growing with the number and the size of the outliers. In the case of unknown outlier location, the dummy-based approach is compared with a robust, mixed Gaussian, quasi maximum likelihood (QML) approach, novel in this context. It is proved that, when the ordinary innovations are Gaussian, the QML and the dummy-based approach are asymptotically equivalent, yielding UR tests with the same asymptotic size and power. Moreover, as a by-product of QML the outlier dates can be consistently estimated. When the innovations display tails fatter than Gaussian, the QML approach ensures further power gains over the dummy-based method. Simulations show that the QML ADF-typet-test, in conjunction with standard Dickey–Fuller critical values, yields the best combination of finite-sample size and power.

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Wilhelm, Daniel. "OPTIMAL BANDWIDTH SELECTION FOR ROBUST GENERALIZED METHOD OF MOMENTS ESTIMATION." Econometric Theory 31, no. 5 (October 2, 2014): 1054–77. http://dx.doi.org/10.1017/s026646661400067x.

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A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are significantly different. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimator’s mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

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Niu, Xijuan, Zhiqiang Pang, and Zhaoxu Wang. "Robust small area estimation for unit level model with density power divergence." PLOS ONE 18, no. 11 (November 16, 2023): e0288639. http://dx.doi.org/10.1371/journal.pone.0288639.

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Unit level model is one of the classical models in small area estimation, which plays an important role with unit information data. Empirical Bayesian(EB) estimation, as the optimal estimation under normal assumption, is the most commonly used parameter estimation method in unit level model. However, this kind of method is sensitive to outliers, and EB estimation will lead to considerable inflation of the mean square error(MSE) when there are outliers in the responses yij. In this study, we propose a robust estimation method for the unit-level model with outliers based on the minimum density power divergence. Firstly, by introducing the minimum density power divergence function, we give the estimation equation of the parameters of the unit level model, and obtain the asymptotic distribution of the robust parameters. Considering the existence of tuning parameters in the robust estimator, an optimal parameter selection algorithm is proposed. Secondly, empirical Bayesian predictors of unit and area mean in finite populations are given, and the MSE of the proposed robust estimators of small area means is given by bootstrap method. Finally, we verify the superior performance of our proposed method through simulation data and real data. Through comparison, our proposed method can can solve the outlier situation better.

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Goryainov, A. V., V. B. Goryainov, and W. M. Khing. "Robust Identification of an Exponential Autoregressive Model." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (91) (August 2020): 42–57. http://dx.doi.org/10.18698/1812-3368-2020-4-42-57.

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One of the most common nonlinear time series (random processes with discrete time) models is the exponential autoregressive model. In particular, it describes such nonlinear effects as limit cycles, resonant jumps, and dependence of the oscillation frequency on amplitude. When identifying this model, the problem arises of estimating its parameters --- the coefficients of the corresponding autoregressive equation. The most common methods for estimating the parameters of an exponential model are the least squares method and the least absolute deviation method. Both of these methods have a number of disadvantages, to eliminate which the paper proposes an estimation method based on the robust Huber approach. The obtained estimates occupy an intermediate position between the least squares and least absolute deviation estimates. It is assumed that the stochastic sequence is described by the autoregressive equation of the first order, is stationary and ergodic, and the probability distribution of the innovations process of the model is unknown. Unbiased, consistency and asymptotic normality of the proposed estimate are established by computer simulation. Its asymptotic variance was found, which allows to obtain an explicit expression for the relative efficiency of the proposed estimate with respect to the least squares estimate and the least absolute deviation estimate and to calculate this efficiency for the most widespread probability distributions of the innovations sequence of the equation of the autoregressive model

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Delpoux, Romain, Thierry Floquet, and Hebertt Sira-Ramírez. "Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only." Automation 2, no. 4 (December 16, 2021): 266–77. http://dx.doi.org/10.3390/automation2040017.

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In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is shown to be robust to noisy measurements and it has the advantage to provide on-line finite-time (or non-asymptotic) state estimations. Based on these estimations, a quasi-homogeneous second-order sliding mode tracking control law including estimated position error integrals is designed illustrating the possibilities of finite-time acceleration feedback via algebraic state estimation.

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Alshahrani, Fatimah, Wahiba Bouabsa, Ibrahim M. Almanjahie, and Mohammed Kadi Attouch. "Robust kernel regression function with uncertain scale parameter for high dimensional ergodic data using $ k $-nearest neighbor estimation." AIMS Mathematics 8, no. 6 (2023): 13000–13023. http://dx.doi.org/10.3934/math.2023655.

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<abstract><p>In this paper, we consider a new method dealing with the problem of estimating the scoring function $ \gamma_a $, with a constant $ a $, in functional space and an unknown scale parameter under a nonparametric robust regression model. Based on the $ k $ Nearest Neighbors ($ k $NN) method, the primary objective is to prove the asymptotic normality aspect in the case of a stationary ergodic process of this estimator. We begin by establishing the almost certain convergence of a conditional distribution estimator. Then, we derive the almost certain convergence (with rate) of the conditional median (scale parameter estimator) and the asymptotic normality of the robust regression function, even when the scale parameter is unknown. Finally, the simulation and real-world data results reveal the consistency and superiority of our theoretical analysis in which the performance of the $ k $NN estimator is comparable to that of the well-known kernel estimator, and it outperforms a nonparametric series (spline) estimator when there are irrelevant regressors.</p></abstract>

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Diehn, Manuel, Axel Munk, and Daniel Rudolf. "Maximum likelihood estimation in hidden Markov models with inhomogeneous noise." ESAIM: Probability and Statistics 23 (2019): 492–523. http://dx.doi.org/10.1051/ps/2018017.

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We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove that the maximum likelihood and a quasi-maximum likelihood estimator (QMLE) are strongly consistent. The computation of the QMLE ignores the inhomogeneity, hence, is much simpler and robust. The theory is motivated by an example from biophysics and applied to a Poisson- and linear Gaussian model.

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She, Y., and K. Chen. "Robust reduced-rank regression." Biometrika 104, no. 3 (July 12, 2017): 633–47. http://dx.doi.org/10.1093/biomet/asx032.

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Summary In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending ψ-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples.

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Kalina, J. "Three contributions to robust regression diagnostics." Journal of Applied Mathematics, Statistics and Informatics 11, no. 2 (December 1, 2015): 69–78. http://dx.doi.org/10.1515/jamsi-2015-0013.

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Abstract Robust regression methods have been developed not only as a diagnostic tool for standard least squares estimation in statistical and econometric applications, but can be also used as self-standing regression estimation procedures. Therefore, they need to be equipped by their own diagnostic tools. This paper is devoted to robust regression and presents three contributions to its diagnostic tools or estimating regression parameters under non-standard conditions. Firstly, we derive the Durbin-Watson test of independence of random regression errors for the regression median. The approach is based on the approximation to the exact null distribution of the test statistic. Secondly, we accompany the least trimmed squares estimator by a subjective criterion for selecting a suitable value of the trimming constant. Thirdly, we propose a robust version of the instrumental variables estimator. The new methods are illustrated on examples with real data and their advantages and limitations are discussed.

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Nugroho, Sebastian A., Ahmad F. Taha, and Junjian Qi. "Robust Dynamic State Estimation of Synchronous Machines With Asymptotic State Estimation Error Performance Guarantees." IEEE Transactions on Power Systems 35, no. 3 (May 2020): 1923–35. http://dx.doi.org/10.1109/tpwrs.2019.2949977.

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Donoho, David, and Andrea Montanari. "High dimensional robust M-estimation: asymptotic variance via approximate message passing." Probability Theory and Related Fields 166, no. 3-4 (November 7, 2015): 935–69. http://dx.doi.org/10.1007/s00440-015-0675-z.

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Zhang, Xiangyu, Jun Sun, and Xingrong Cao. "Robust direction-of-arrival estimation based on sparse asymptotic minimum variance." Journal of Engineering 2019, no. 21 (November 1, 2019): 7815–21. http://dx.doi.org/10.1049/joe.2019.0720.

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Xia, Jingping, Bin Jiang, and Ke Zhang. "Robust Asymptotic Estimation of Sensor Faults for Continuous-time Interconnected Systems." International Journal of Control, Automation and Systems 17, no. 12 (December 2019): 3170–78. http://dx.doi.org/10.1007/s12555-019-0270-7.

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Knüfer, Sven, and Matthias A. Müller. "Nonlinear full information and moving horizon estimation: Robust global asymptotic stability." Automatica 150 (April 2023): 110603. http://dx.doi.org/10.1016/j.automatica.2022.110603.

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Khan, Zahid, Katrina Lane Krebs, Sarfaraz Ahmad, and Misbah Munawar. "POWER SYSTEM STATE ESTIMATION USING A ROBUST ESTIMATOR." NED University Journal of Research XVI, no. 4 (August 30, 2019): 53–65. http://dx.doi.org/10.35453/nedjr-ascn-2018-0038.

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State estimation (SE) is a primary data processing algorithm which is utilised by the control centres of advanced power systems. The most generally utilised state estimator is based on the weighted least squares (WLS) approach which is ineffective in addressing gross errors of input data of state estimator. This paper presents an innovative robust estimator for SE environments to overcome the non-robustness of the WLS estimator. The suggested approach not only includes the similar functioning of the customary loss function of WLS but also reflects loss function built on the modified WLS (MWLS) estimator. The performance of the proposed estimator was assessed based on its ability to decrease the impacts of gross errors on the estimation results. The properties of the suggested state estimator were investigated and robustness of the estimator was studied considering the influence function. The effectiveness of the proposed estimator was demonstrated with the help of examples which also indicated non-robustness of MWLS estimator in SE algorithm.

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Koo, Bonsoo, and Oliver Linton. "LET’S GET LADE: ROBUST ESTIMATION OF SEMIPARAMETRIC MULTIPLICATIVE VOLATILITY MODELS." Econometric Theory 31, no. 4 (November 5, 2014): 671–702. http://dx.doi.org/10.1017/s0266466614000516.

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We investigate a model in which we connect slowly time varying unconditional long-run volatility with short-run conditional volatility whose representation is given as a semi-strong GARCH(1,1) process with heavy tailed errors. We focus on robust estimation of both long-run and short-run volatilities. Our estimation is semiparametric since the long-run volatility is totally unspecified whereas the short-run conditional volatility is a parametric semi-strong GARCH(1,1) process. We propose different robust estimation methods for nonstationary and strictly stationary GARCH parameters with nonparametric long-run volatility function. Our estimation is based on a two-step LAD procedure. We establish the relevant asymptotic theory of the proposed estimators. Numerical results lend support to our theoretical results.

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Wang, Andong, Chao Li, Zhong Jin, and Qibin Zhao. "Robust Tensor Decomposition via Orientation Invariant Tubal Nuclear Norms." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6102–9. http://dx.doi.org/10.1609/aaai.v34i04.6074.

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Low-rank tensor recovery has been widely applied to computer vision and machine learning. Recently, tubal nuclear norm (TNN) based optimization is proposed with superior performance as compared to other tensor nuclear norms. However, one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations. To this end, we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way (K ≥ 3) tensors. We further formulate two robust tensor decomposition models via the proposed norms and develop two algorithms as the solutions. Theoretically, we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error. Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.

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Khooban, M. H., M. Siahi, and M. R. Soltanpour. "Robust and simple intelligent observer-based fault estimation and reconstruction for a class of non-linear systems: HIRM aircraft." Aeronautical Journal 120, no. 1225 (March 2016): 457–72. http://dx.doi.org/10.1017/aer.2016.5.

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ABSTRACTThis paper introduces an observer strategy, namely a Sliding Mode Observer (SMO), to realise the fault detection and estimation of general uncertain non-linear systems. The use of a non-linear observer is considered for monitoring the states of a high incidence research model (HIRM) aircraft system. For a special class of Lipschitz non-linear system, a fault reconstruction scheme is presented where the reconstructed signal can approximate the fault signal to any accuracy. The proposed method is based only on the available plant input-output information and can be calculated online. Moreover, the globally asymptotic stability of the closed-loop system is mathematically proved. Finally, an HIRM aircraft system example is given to illustrate the efficiency of the proposed approach.

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Li, Zhijun, Minxing Sun, Qianwen Duan, and Yao Mao. "Robust State Estimation for Uncertain Discrete Linear Systems with Delayed Measurements." Mathematics 10, no. 9 (April 19, 2022): 1365. http://dx.doi.org/10.3390/math10091365.

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Measurement delays and model parametric uncertainties are meaningful issues in actual systems. Addressing the simultaneous existence of random model parametric uncertainties and constant measurement delay in the discrete-time linear systems, this study proposes a novel robust estimation method based on the combination of Kalman filter regularized least-squares (RLS) framework and state augmentation. The state augmentation method is elaborately designed, and the cost function is improved by considering the influence of modelling errors. A recursive program similar to the Kalman filter is derived. Meanwhile, the asymptotic stability conditions of the proposed estimator and the boundedness conditions of its error covariance are analyzed theoretically. Numerical simulation results show that the proposed method has a better processing capability for measurement delay and better robustness to model parametric uncertainties than the Kalman filter based on nominal parameters.

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Andrews, Donald W. K., and Xu Cheng. "GMM ESTIMATION AND UNIFORM SUBVECTOR INFERENCE WITH POSSIBLE IDENTIFICATION FAILURE." Econometric Theory 30, no. 2 (November 29, 2013): 287–333. http://dx.doi.org/10.1017/s0266466613000315.

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This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CSs) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CSs are established.The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald,t, and quasi-likelihood ratio tests and CSs whose critical values are designed to yield robustness to identification problems.The results of the paper are applied to a nonlinear regression model with endogeneity and a probit model with endogeneity and possibly weak instrumental variables.

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Hu, Weijun. "Nonlinear augmented state observer-based adaptive output feedback anti-disturbance control for nonlinear systems with non-harmonic multiple uncertainties." Transactions of the Institute of Measurement and Control 41, no. 7 (August 20, 2018): 1904–11. http://dx.doi.org/10.1177/0142331218790099.

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In this paper, a novel output feedback anti-disturbance control method is carried out for a class of nonlinear systems subject to non-harmonic multisource disturbances. By using a nonlinear exogenous system, a class of non-harmonic disturbances possessing complex and nonlinear characteristics are taken fully into consideration. Based on a nonlinear damping term, we establish an adaptive augmented state observer that can achieve robust asymptotic disturbance estimation for the system states, the harmonic disturbances and the non-harmonic disturbances. By fusing the augmented state observer and a state-feedback controller, a robust adaptive output feedback anti-disturbance control structure is constructed. The boundness of the combined controller–observer system is derived on the basis of Lyapunov analysis. Furthermore, aiming at the intense non-harmonic disturbances, the proposed method is extended and a new output feedback controller is obtained. The effectiveness of the proposed scheme is demonstrated through experimental studies on a practical example.

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Journal articles on the topic 'Non-Asymptotic and robust estimation'

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