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A0205
Title: PMSE performance of two different types of preliminary test estimators under a multivariate $t$ error Authors:  Haifeng Xu - Xiamen University (China) [presenting]
Kazuhiro Ohtani - kobe university (Japan)
Abstract: Assuming that the error terms follow a multivariate $t$ distribution, the exact formula is derived for the predictive mean squared error (PMSE) of two different types of preliminary test estimators: (1) a homogeneous pre-test (HO-PT) estimator whose components are the adjusted minimum mean squared error (AMMSE) estimator and the minimum mean squared error (MMSE) estimator; (2) a heterogeneous pre-test (HE-PT) estimator whose components are the AMMSE estimator and the Stein-rule (SR) estimator. It is shown analytically that the HE-PT estimator dominates the SR estimator if a critical value of the pre-test is chosen appropriately. Also, we compare the PMSE of the HO-PT, HE-PT, MMSE, AMMSE, SR and PSR estimators by numerical evaluations. Our results show that 1. the HO-PT and HE-PT estimators dominate the OLS estimator for all combinations when the degrees of freedom is not more than 5; 2. if the number of independent variables is 3, and the critical value of the pre-test is chosen appropriately, then the HE-PT estimator dominates the PSR estimator even when error terms follow a multivariate $t$ distribution.