Estimating the structural dimension of regressions via parametric inverse regression

• 成果类型: Article
• 署名作者: Bura, E; Cook, RD
• 署名单位: George Washington University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/1467-9868.00292
• 发表日期: 2001
• 页码: 393-410
• 关键词: principal hessian directions; reduction

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.