Preliminary Test Estimators for the Multivariate Normal Mean Based on The Modified W, LR and LM Tests
S. Khan and Z. Hoque (2003). Preliminary Test Estimators for the Multivariate Normal Mean Based on The Modified W, LR and LM Tests. Journal of Statistical Research, Vol. 37, No. 1, pp. 43-55.
In this paper we consider the preliminary test estimators (PTEs) of the mean vector of multivariate normal distribution under the modied Wald, likelihood ratio, and Lagrange multiplier tests. The properties of the estimators have been investigated under some popular statistical criteria. It has been observed that with respect to the quadratic bias the Wald test based PTE performs better than those based on the likelihood ratio and Lagrange multiplier tests. Whereas, with respect to the quadratic risk the Lagrange multiplier test based PTE performs better than those based on the likelihood ratio and Wald tests. The results of this study reveal that the use of the three modied tests in the formation of the PTEs signicantly reduces the con ict among the PTEs as compared to the estimators based on the three original tests in terms of both quadratic bias and risk properties.
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