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Further research on the principal component two-parameter estimator in linear model

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  • Hu Yang
  • Jiewu Huang

Abstract

In this article, we introduce a generalized Mahalanobis loss function which can be applied to the estimator for regression coefficients whether its covariance matrix is singular or non singular. Then, we give detailed comparisons between those estimators that can be derived from the principal component two-parameter estimator under the generalized Mahalanobis loss function by the average loss criterion. Also, we obtain conditions for the superiority of one estimator over the other and propose the optimal values for ridge parameter k and Liu parameter d. Furthermore, we illustrate the theoretical results by a numerical example and a Monte Carlo simulation study.

Suggested Citation

  • Hu Yang & Jiewu Huang, 2016. "Further research on the principal component two-parameter estimator in linear model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 566-576, February.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:3:p:566-576
    DOI: 10.1080/03610926.2013.833237
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