TY - JOUR
T1 - Extending sliced inverse regression
T2 - The weighted chi-squared test
AU - Bura, Efstathia
AU - Cook, R. Dennis
PY - 2001/9/1
Y1 - 2001/9/1
N2 - 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. 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.
AB - 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. 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.
KW - Dimension estimation
KW - Dimension reduction
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U2 - 10.1198/016214501753208979
DO - 10.1198/016214501753208979
M3 - Article
AN - SCOPUS:0442280663
SN - 0162-1459
VL - 96
SP - 996
EP - 1003
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 455
ER -