Comparison of the r - (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function

International Econometric Review

卷:7

Shalini Chandra¹  Nityananda Sarkar² 

[1] Banasthali University ;

[2] Indian Statistical Institute;

关键词: r - (k;    d) class estimator;    Principal component estimator;    Two-parameter class estimator;    Mahalanobis loss function;    Risk criterion;   

DOI  :  

来源: DOAJ

【 摘 要 】

In the case of ill-conditioned design matrix in linear regression model, the r - (k, d) classestimator was proposed, including the ordinary least squares (OLS) estimator, theprincipal 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 incomparison to others under the weighted quadratic loss function where the weights areinverse of the variance-covariance matrix of the estimator, also known as theMahalanobis loss function using the criterion of average loss. Tests verifying theconditions 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 theperformance 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 artificiallygenerated data sets and as well as for a real data. To the best of our knowledge, this studyprovides stronger evidence of superiority of the r - (k, d) class estimator over the othercompeting estimators through tests for verifying the conditions of dominance, available inliterature on multicollinearity.

【 授权许可】

Unknown