A new approach on recursive and non-recursive SIR methods

被引:0
作者
Bernard Bercu
Thi Mong Ngoc Nguyen
Jérôme Saracco
机构
[1] Université de Bordeaux,Institut de Mathématiques de Bordeaux, UMR CNRS 5251
[2] INRIA Bordeaux Sud-Ouest,ALEA team
[3] NRIA Bordeaux Sud-Ouest,CQFD team
[4] Institut Polytechnique de Bordeaux,undefined
来源
Journal of the Korean Statistical Society | 2012年 / 41卷
关键词
primary 62H99; secondary 62F99; Recursive estimation; Semiparametric regression model; Sliced inverse regression (SIR);
D O I
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中图分类号
学科分类号
摘要
We consider a semiparametric single index regression model involving a p-dimensional quantitative covariable x and a real dependent variable y. A dimension reduction is included in this model via an index x′β. Sliced inverse regression (SIR) is a well-known method to estimate the direction of the Euclidean parameter β which is based on a “slicing step” of y in the population and sample versions. The goal of this paper is twofold. On the one hand, we focus on a recursive version of SIR which is also suitable for multiple indices model. On the other hand, we propose a new method called SIRoneslice when the regression model is a single index model. The SIRoneslice estimator of the direction of β is based on the use of only one “optimal” slice chosen among the H slices. Then, we provide its recursive version. We give an asymptotic result for the SIRoneslice approach. Simulation study shows good numerical performances of the SIRoneslice method and clearly exhibits the main advantage of using recursive versions of the SIR and SIRoneslice methods from a computational time point of view. A real dataset is also used to illustrate the approach. Some extensions are discussed in concluding remarks. The proposed methods and criterion have been implemented in R and the corresponding codes are available from the authors.
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页码:17 / 36
页数:19
相关论文
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