Template-Type: ReDIF-Article 1.0
Author-Name:  Shalini Chandra
Author-Email: chandrshalini@gmail.com
Author-Workplace-Name: Banasthali University, Centre for Mathematical Sciences, India.
Author-Name:  Nityananda Sarkar
Author-Email: tanya@isical.ac.in
Author-Workplace-Name: Indian Statistical Institute, India.
Title:  Comparison of the r - (k, d) Class Estimator with some Estimators for Multicollinearity under the Mahalanobis Loss Function
Abstract:  In the case of ill-conditioned design matrix in linear regression model, the r - (k, d) class estimator was proposed, including the ordinary least squares (OLS) estimator, the
principal component regression (PCR) estimator, and the two-parameter class estimator. In this paper, we opted to evaluate the performance of the r - (k, d) class estimator in
comparison to others under the weighted quadratic loss function where the weights are inverse of the variance-covariance matrix of the estimator, also known as the
Mahalanobis loss function using the criterion of average loss. Tests verifying the conditions for superiority of the r - (k, d) class estimator have also been proposed. Finally,
a simulation study and also an empirical illustration have been done to study the performance of the tests and hence verify the conditions of dominance of the r - (k, d)
class estimator over the others under the Mahalanobis loss function in artificially generated data sets and as well as for a real data. To the best of our knowledge, this study
provides stronger evidence of superiority of the r - (k, d) class estimator over the other competing estimators through tests for verifying the conditions of dominance, available in
literature on multicollinearity.
Keywords: r - (k, d) class estimator, Principal component estimator, Two-parameter class estimator, Mahalanobis loss function, Risk criterion
Journal: International Econometric Review
Pages: 1-12
Volume: 7
Issue: 1
Year: 2015
Month: April
File-URL: http://www.era.org.tr/makaleler/27020097.pdf
File-Format: Application/pdf
Handle: RePEc:erh:journl:v:7:y:2015:i:1:p:1-12