Risk comparison of some shrinkage M-estimators in linear models

The problem of robust estimation of a (linear) regression parameter (vector), in the presence of nuisance scale parameter, is considered when it is a priori suspected that the regression could be restricted to a linear subspace. Asymptotic properties of variants of Stein-rule M-estimators (including the positive-rule shrinkage M-estimators) are studied. Under an asymptotic distributional quadratic risk criterion, their relative dominance picture is explored, analytically as well as by simulation. An extensive sampling experiment is used to examine the small sample characteristics of the proposed estimators over a wide-range of data sampling designs and distributions. Our simulation experiments have provided strong evidence that corroborates with the asymptotic theory. Two examples are provided to illustrate the performance of the estimators in real-life situations.

[1]  S. E. Ahmed,et al.  Large‐Sample Pooling Procedure for Correlation , 1992 .

[2]  S. E. Ahmed,et al.  Improved biased estimation in an ANOVA model , 1999 .

[3]  P. J. Huber.  Robust Statistical Procedures , 1977 .

[4]  C. Morris,et al.  Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution , 1972 .

[5]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[6]  P. Sen,et al.  On preliminary test and shrinkage m-estimation in linear models , 1987 .

[7]  Pranab Kumar Sen,et al.  On the asymptotic distributional risks of shrinkage and preliminary test versions of maximum likelihood estimators , 1984 .

[8]  S. E. Ahmed,et al.  Simultaneous estimation of coefficients of variation , 2002 .

[9]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[10]  Stephen M. Stigler,et al.  The 1988 Neyman Memorial Lecture: A Galtonian Perspective on Shrinkage Estimators , 1990 .

[11]  T. Hettmansperger,et al.  Robust Nonparametric Statistical Methods , 1998 .

[12]  Paul W. Holland,et al.  Two Robust Alternatives to Least-Squares Regression , 1977 .

[13]  T. Kubokawa.  The Stein Phenomenon in Simultaneous Estimation: A Review , 1997 .

[14]  S. E. Ahmed.  Assessing the process capability index for non-normal processes , 2005 .

[15]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[16]  Rand R. Wilcox,et al.  The statistical implications of pre-test and Stein-rule estimators in econometrics , 1978 .

[17]  S. E. Ahmed.  Shrinkage Estimation of Regression Coefficients From Censored Data With Multiple Observations , 2001 .

[18]  R. W. Farebrother,et al.  The statistical implications of pre-test and Stein-rule estimators in econometrics , 1978 .

[19]  T. Hettmansperger,et al.  Robust analysis of variance based upon a likelihood ratio criterion , 1980 .