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RISS 인기검색어
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- 저자 : Jérôme Saracco (검색결과 2 건)
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Cluster-based Sliced Inverse Regression
Jérôme Saracco,Vanessa Kuentz 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.2
In the theory of sufficient dimension reduction, Sliced Inverse Regression (SIR) is a famous technique that enables us to reduce the dimensionality of regression problems. This semiparametric regression method aims at determining linear combinations of a pdimensional explanatory variable x related to a response variable y. However it is based on a crucial condition on the marginal distribution of the predictor x, often called the linearity condition. From a theoretical and practical point of view, this condition appears to be a limitation. Using an idea of Li, Cook, and Nachtsheim (2004) in the Ordinary Least Squares framework, we propose in this article to cluster the predictor space so that the linearity condition approximately holds in the different partitions. Then we apply SIR in each cluster and finally estimate the dimension reduction subspace by combining these individual estimates. We give asymptotic properties of the corresponding estimator. We show with a simulation study that the proposed approach, referred as cluster-based SIR,improves the estimation of the e.d.r. basis. We also propose an iterative implementation of cluster-based SIR and show in simulations that it increases the quality of the estimator. Finally the methodology is applied on the horse mussel data and the comparison of the prediction reached on test samples shows the superiority of cluster-based SIR over SIR.
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A new approach on recursive and non-recursive SIR methods
Bernard Bercu,Thi Mong Ngoc Nguyen,Jérôme Saracco 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.1
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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