Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.

[1]  A. V. Dorugade.  EFFICIENT TWO-PARAMETER ESTIMATOR IN LINEAR REGRESSION MODEL , 2019, Statistics in Transition New Series.

[2]  Stan Lipovetsky,et al.  Two-parameter ridge regression and its convergence to the eventual pairwise model , 2006, Math. Comput. Model..

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

[4]  Hasan Ertas,et al.  A modified ridge m-estimator for linear regression model with multicollinearity and outliers , 2018, Commun. Stat. Simul. Comput..

[5]  Gülesen Üstündağ Şiray,et al.  Restricted Two Parameter Ridge Estimator , 2013 .

[6]  Stan Lipovetsky,et al.  Ridge regression in two‐parameter solution , 2005 .

[7]  Selahattin Kaçiranlar,et al.  On the performance of two parameter ridge estimator under the mean square error criterion , 2013, Appl. Math. Comput..

[8]  A. Lukman,et al.  A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications , 2020, Scientifica.

[9]  Insha Ullah,et al.  Insha's Redescending M-estimator for Robust Regression: A Comparative Study , 2006 .

[10]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[11]  M. Norouzirad,et al.  Preliminary test and Stein-type shrinkage ridge estimators in robust regression , 2017 .

[12]  I. Dawoud,et al.  THE PREDICTION OF THE TWO PARAMETER RIDGE ESTIMATOR , 2016 .

[13]  A MODIFIED TWO-PARAMETER ESTIMATOR IN LINEAR REGRESSION , 2014 .

[14]  Nimet Özbay.  Two-Parameter Ridge Estimation for the Coefficients of Almon Distributed Lag Model , 2018, Iranian Journal of Science and Technology, Transactions A: Science.

[15]  E. Almetwally,et al.  • COMPARISON BETWEEN M-ESTIMATION, S-ESTIMATION, AND MM ESTIMATION METHODS OF ROBUST ESTIMATION WITH APPLICATION AND SIMULATION , 2018 .

[16]  Kristofer Månsson,et al.  Modified Ridge Regression Estimators , 2013 .

[17]  Selma Toker,et al.  Robust two parameter ridge M-estimator for linear regression , 2015 .

[18]  B. M. Golam Kibria,et al.  Quantile-based robust ridge m-estimator for linear regression model in presence of multicollinearity and outliers , 2019, Commun. Stat. Simul. Comput..

[19]  D. N. Kashid,et al.  Robust Linearized Ridge M-estimator for Linear Regression Model , 2016, Commun. Stat. Simul. Comput..

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