Evaluation of the Goldfeld-Quandt test and alternatives (original) (raw)
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summary This paper deflnes the preliminary test estimator (PTE) of the univariate normal mean under the original as well as the Edgeworth size corrected Wald (W), likelihood ratio (LR) and Lagrange multiplier (LM) tests. The bias and mean squared error (MSE) functions of the estimators are derived. The con∞icts among the biases and the MSEs of the PTEs under the three original and the size corrected tests have been obtained. It is found that instead of the original W, LR and LM tests, the use of the Edgeworth size corrected W, LR and LM tests in the formation of the PTEs reduces the con∞ict among the biases and MSEs of the estimators remarkably.
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Author Contact: Lauren Dong, Statistics Canada; e-mail: Lauren.Dong@statcan.can; FAX: (613) 951-3292 David Giles*, Dept. of Economics, University of Victoria, P.O. Box 1700, STN CSC, Victoria, B.C., Canada V8W 2Y2; e-mail: dgiles@uvic.ca; FAX: (250) 721-6214 * Corresponding co-author Abstract The empirical likelihood ratio (ELR) test for the problem of testing for normality in a linear regression model is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are explored and analyzed using Monte Carlo simulation. The ELR test has good power properties against various alternative hypotheses.
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In this paper we consider the preliminary test estimators (PTEs) of the mean vector of multivariate normal distribution under the modified 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 modified tests in the formation of the PTEs significantly reduces the conflict 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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