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

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.

KEYWORDS:

• Feasible ridge regression estimator
• Heterogeneous preliminary test estimator
• MSE performance
• Multivariate t distribution
• Optimal critical value

Acknowledgments

I would like to thank Kazuhiro Ohtani for his guidance and suggestions. I would also like to thank Akio Namba and an anonymous referee for their useful comments.

Notes

1 The double k-class estimator is proposed by Ullah and Ullah (1978).

2 and are quadratic risk functions (MSE) for the FRR () and the OLS estimator (b₁), respectively.