×

Approximating null distribution of the M-test statistics in linear models. (English) Zbl 1174.62331

Summary: Linear hypotheses in linear models can be tested by the M-method. The M-test, the Wald-type test (W-test) and Rao’s score-type test (R-test) are the three most commonly used testing methods. However, the critical values for these tests are usually related to the unknown error distribution. We propose random weighting resampling methods for approximating the null distribution of these tests. It is shown that under both the null and local alternatives these random weighting test statistics all have the same asymptotic null distributions as for the original test statistic. The critical values of these tests can therefore be obtained by the Monte Carlo random weighting method.
An important feature of the proposed methods is that the approximations are valid even when the null hypothesis is not true and the power evaluation is possible under the local alternatives. We made extensive simulations under different error distribution specifications and different choices of the random weighting variables to assess the performance of the proposed method. The results show that the random weighting M-testing method can provide good accurate approximations of the null distributions.

MSC:

62F05 Asymptotic properties of parametric tests
62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
62F10 Point estimation
PDFBibTeX XMLCite