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Robust bounded-influence tests in linear models. (English) Zbl 0712.62029
A robust test that we call an aligned generalized M test for testing subhypotheses in general linear models is developed, and its asymptotic properties are studied. The test is a robustification of the well-known F test. p-values associated with it can be approximated readily using existing chi-square tables. The test is based on an appropriately constructed quadratic form and uses the generalized M estimators of the parameters in the reduced model. Under the null hypothesis the asymptotic distribution is a central chi square, and under contiguous alternatives it is a noncentral chi square with the same degrees of freedom. The test can be viewed as a generalization of P. K. Sen’s [Biometrica 69, 245-248 (1982; Zbl 0483.62016)] M test for linear models.

62F35 Robustness and adaptive procedures (parametric inference)
62F03 Parametric hypothesis testing
62J99 Linear inference, regression
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