A Comparison of Partially Adaptive and Reweighted Least Squares Estimation

Abstract The small sample performance of least median of squares, reweighted least squares, least squares, least absolute deviations, and three partially adaptive estimators are compared using Monte Carlo simulations. Two data problems are addressed in the paper: (1) data generated from non‐normal error distributions and (2) contaminated data. Breakdown plots are used to investigate the sensitivity of partially adaptive estimators to data contamination relative to RLS. One partially adaptive estimator performs especially well when the errors are skewed, while another partially adaptive estimator and RLS perform particularly well when the errors are extremely leptokur‐totic. In comparison with RLS, partially adaptive estimators are only moderately effective in resisting data contamination; however, they outperform least squares and least absolute deviation estimators.

[1]  Stefan Van Aelst,et al.  Robust Multivariate Regression , 2004, Technometrics.

[2]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[3]  R. Dennis Cook,et al.  Detection of Influential Observation in Linear Regression , 2000, Technometrics.

[4]  James B. McDonald,et al.  A generalization of the beta distribution with applications , 1995 .

[5]  Sangit Chatterjee,et al.  An Outlier-Resistant Approach to Risk Estimation , 1994 .

[6]  Daniel B. Nelson,et al.  ARCH MODELS a , 1994 .

[7]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[8]  James B. McDonald,et al.  A comparison of some robust, adaptive, and partially adaptive estimators of regression models , 1993 .

[9]  Xuming He.  TAIL BEHAVIOR OF REGRESSION ESTIMATORS AND THEIR BREAKDOWN POINTS , 1990 .

[10]  Richard J. Butler,et al.  Robust and Partially Adaptive Estimation of Regression Models , 1990 .

[11]  D. Pollard,et al.  Cube Root Asymptotics , 1990 .

[12]  P. Rousseeuw,et al.  Unmasking Multivariate Outliers and Leverage Points , 1990 .

[13]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[14]  James B. McDonald,et al.  Partially Adaptive Estimation of Regression Models via the Generalized T Distribution , 1988, Econometric Theory.

[15]  Whitney K. Newey,et al.  Adaptive estimation of regression models via moment restrictions , 1988 .

[16]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[17]  T. Bollerslev,et al.  A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN , 1987 .

[18]  Charles F. Manski,et al.  Monte Carlo evidence on adaptive maximum likelihood estimation of a regression , 1987 .

[19]  John Law,et al.  Robust Statistics—The Approach Based on Influence Functions , 1986 .

[20]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[21]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[22]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[23]  W. Steiger,et al.  Least Absolute Deviations: Theory, Applications and Algorithms , 1984 .

[24]  Subhash C. NarulaI,et al.  The Minimum Sum of Absolute Errors Regression: A State of the Art Survey , 1982 .

[25]  A. Siegel.  Robust regression using repeated medians , 1982 .

[26]  F. Hampel.  The Influence Curve and Its Role in Robust Estimation , 1974 .

[27]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[28]  F. Black,et al.  The Capital Asset Pricing Model: Some Empirical Tests , 2006 .

[29]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[30]  G. C. Tiao,et al.  A Further Look at Robustness via Bayes's Theorem , 1962 .