Estimating the structural dimension of regressions via parametric inverse regression

被引：104
作者：
Bura, E
Cook, RD
机构：
[1] George Washington Univ, Dept Stat, Washington, DC 20052 USA
[2] Univ Minnesota, St Paul, MN 55108 USA
来源：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY | 2001年 / 63卷
关键词：
asymptotic test for dimension; dimension reduction; inverse regression; parametric inverse regression; sliced inverse regression;
D O I：
10.1111/1467-9868.00292
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
A new estimation method for the dimension of a regression at the outset of an analysis is proposed. A linear subspace spanned by projections of the regressor vector X, which contains part or all of the modelling information for the regression of a vector Y on X, and its dimension are estimated via the means of parametric inverse regression. Smooth parametric curves are fitted to the p inverse regressions via a multivariate linear model. No restrictions are placed on the distribution of the regressors. The estimate of the dimension of the regression is based on optimal estimation procedures. A simulation study shows the method to be more powerful than sliced inverse regression in some situations.
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页码：393 / 410
页数：18
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