Bura, Efstathia; Cook, R. Dennis Extending sliced inverse regression: The weighted chi-squared test. (English) Zbl 1047.62035 J. Am. Stat. Assoc. 96, No. 455, 996-1003 (2001). 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. Cited in 60 Documents MSC: 62G10 Nonparametric hypothesis testing 62J99 Linear inference, regression 62H10 Multivariate distribution of statistics Keywords:dimension estimation; dimension reduction Citations:Zbl 0742.62044 PDFBibTeX XMLCite \textit{E. Bura} and \textit{R. D. Cook}, J. Am. Stat. Assoc. 96, No. 455, 996--1003 (2001; Zbl 1047.62035) Full Text: DOI