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Extending sliced inverse regression: The weighted chi-squared test. (English) Zbl 1047.62035
Summary: Sliced inverse regression (SIR) and an associated chi-squared test for dimension have been introduced as a method for reducing the dimension of regression problems whose predictor variables are normal [see K.-C. Li, ibid. 86, No. 414, 316–342 (1991; Zbl 0742.62044)]. In this article, the assumptions on the predictor distribution, under which the chi-squared test was proved to apply, are relaxed, and the result is extended. A general weighted chi-squared test that does not require normal regressors for the dimension of a regression is given. Simulations show that the weighted chi-squared test is more reliable than the chi-squared test when the regressor distribution digresses from normality significantly, and that it compares well with the chi-squared test when the regressors are normal.

62G10 Nonparametric hypothesis testing
62J99 Linear inference, regression
62H10 Multivariate distribution of statistics
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