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MSE performance and minimax regret significance points for a HPT estimator under a multivariate t error distribution

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  • Haifeng Xu

Abstract

In this article, assuming that the error terms follow a multivariate t distribution,we derive the exact formulae forthe moments of the heterogeneous preliminary test (HPT) estimator proposed by Xu (2012b). We also execute the numerical evaluation to investigate the mean squared error (MSE) performance of the HPT estimator and compare it with those of the feasible ridge regression (FRR) estimator and the usual ordinary least squared (OLS) estimator. Further, we derive the optimal critical values of the preliminary F test for the HPT estimator, using the minimax regret function proposed by Sawa and Hiromatsu (1973). Our results show that (1) the optimal significance level (α*) increases as the degrees of freedom of multivariate t distribution (ν0) increases; (2) when ν0 ⩾ 10, the value of α* is close to that in the normal error case.

Suggested Citation

  • Haifeng Xu, 2017. "MSE performance and minimax regret significance points for a HPT estimator under a multivariate t error distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3123-3134, April.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:7:p:3123-3134
    DOI: 10.1080/03610926.2015.1056364
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