Robust Liu-type estimator for regression based on M-estimator

ABSTRACT The problem of multicollinearity and outliers in the dataset can strongly distort ordinary least-square estimates and lead to unreliable results. We propose a new Robust Liu-type M-estimator to cope with this combined problem of multicollinearity and outliers in the y-direction. Our new estimator has advantages over two-parameter Liu-type estimator, Ridge-type M-estimator, and M-estimator. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.

[1]  J. Neyman,et al.  INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION , 2005 .

[2]  Jammalamadaka.  Introduction to Linear Regression Analysis (3rd ed.) , 2003 .

[3]  Arthur E. Hoerl,et al.  Ridge Regression: Biased Estimation for Nonorthogonal Problems , 2000, Technometrics.

[4]  G. C. McDonald,et al.  A Monte Carlo Evaluation of Some Ridge-Type Estimators , 1975 .

[5]  Liu Kejian,et al.  A new class of blased estimate in linear regression , 1993 .

[6]  J. Brian Gray,et al.  Introduction to Linear Regression Analysis , 2002, Technometrics.

[7]  D. Gibbons.  A Simulation Study of Some Ridge Estimators , 1981 .

[8]  Fikri Akdeniz,et al.  On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse , 1995 .

[9]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[10]  Kejian Liu.  Using Liu-Type Estimator to Combat Collinearity , 2003 .

[11]  Nedret Billor,et al.  Robust Liu estimator for regression based on an M-estimator , 2000 .

[12]  Mervyn J. Silvapulle,et al.  ROBUST RIDGE REGRESSION BASED ON AN M-ESTIMATOR , 1991 .

[13]  B. M. Kibria,et al.  Performance of Some New Ridge Regression Estimators , 2003 .

[14]  A. E. Hoerl,et al.  Ridge regression:some simulations , 1975 .

[15]  R. H. Myers.  Classical and modern regression with applications , 1986 .

[16]  C. Jennison,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .