Comparison of the r - (k, d) Class Estimator with some Estimators for Multicollinearity under the Mahalanobis Loss Function

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.