Team cqfd

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Section: New Results

Recursive and non recursive versions for SIR and SIRoneslice (a new one slice-based SIR approach)

Participants : Bernard Bercu, Thi Mong Ngoc Nguyen, Jérôme Saracco.

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'$ \beta$ . Sliced inverse regression (SIR) is a well-known method to estimate the direction of the euclidean parameter $ \beta$ which is based on a “slicing step” of y in the population and sample versions. The goal of this work is twofold. We first propose an estimator of the direction of $ \beta$ based on the use of only one “optimal” slice chosen among the H slices. We call this new method SIRoneslice. Then we provide the recursive versions of the SIR and SIRoneslice estimators. We give an asymptotic result for SIRoneslice approach. Simulation study shows good numerical performances of SIRoneslice method and clearly exhibits the main advantage of using recursive versions of the SIR and SIRoneslice methods from a computational times point of view. Some extensions are also discussed. The proposed methods and criterion have been implemented in R and the corresponding codes are available from the authors. This work is in revision for publication [12] .


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