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

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  • Shalini Chandra

    (Banasthali University, Centre for Mathematical Sciences, India.)

  • Nityananda Sarkar

    (Indian Statistical Institute, India.)

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.

Suggested Citation

  • Shalini Chandra & Nityananda Sarkar, 2015. "Comparison of the r - (k, d) Class Estimator with some Estimators for Multicollinearity under the Mahalanobis Loss Function," International Econometric Review (IER), Econometric Research Association, vol. 7(1), pages 1-12, April.
    • Handle: RePEc:erh:journl:v:7:y:2015:i:1:p:1-12
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    References listed on IDEAS

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    1. Sarkar, Nityananda, 1996. "Mean square error matrix comparison of some estimators in linear regressions with multicollinearity," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 133-138, October.
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    Cited by:

    1. Shalini Chandra & Gargi Tyagi, 2017. "On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors," Statistics in Transition New Series, Polish Statistical Association, vol. 18(1), pages 27-52, March.
    2. Chandra Shalini & Tyagi Gargi, 2017. "On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors," Statistics in Transition New Series, Polish Statistical Association, vol. 18(1), pages 27-52, March.

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