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Preliminary test Liu estimators based on the conflicting W, LR and LM tests in a regression model with multivariate Student-\(t\) error. (English) Zbl 1213.62031

Summary: The problem of estimation of the regression coefficients in a multiple regression model with multivariate Student-\(t\) errors is considered under the multicollinearity situation when it is suspected that the regression coefficients may be restricted to a linear manifold. The preliminary test K. Liu [Commun. Stat., Theory Methods 22, No. 2, 393–402 (1993; Zbl 0784.62065)] estimators (PTLE) based on the Wald, likelihood ratio (LR) and Lagrangian multiplier (LM) tests are given. The bias and mean square error (MSE) of the proposed estimators are derived and conditions of superiority of these estimators are provided. In particular, we show that in the neighborhood of the null hypothesis, the PTLE based on the LM test has the best performance followed by the estimators based on LR and W tests, while the situation is reversed when the parameter moves away from the manifold of the restriction. Furthermore, the optimum choice of the level of significance is also discussed.

MSC:

62F03 Parametric hypothesis testing
62J05 Linear regression; mixed models
62F10 Point estimation
62F30 Parametric inference under constraints
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 0784.62065
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References:

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