Optimal quantization applied to sliced inverse regression

In this paper we consider a semiparametric regression model involving a d-dimensional quantitative explanatory variable X and including a dimension reduction of X via an index β ′ X . In this model, the main goal is to estimate the Euclidean parameter β and to predict the real response variable Y co...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2012-02, Vol.142 (2), p.481-492
Main Authors: Azaïs, Romain, Gégout-Petit, Anne, Saracco, Jérôme
Format: Article
Language:English
Subjects:
Exact sciences and technology
Functional analysis
General topics
Linear inference, regression
Mathematical analysis
Mathematics
Optimal quantization
Probability and statistics
Reduction dimension
Sampling theory, sample surveys
Sciences and techniques of general use
Semiparametric regression model
Sliced inverse regression (SIR)
Statistics
Statistics Theory
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Summary:In this paper we consider a semiparametric regression model involving a d-dimensional quantitative explanatory variable X and including a dimension reduction of X via an index β ′ X . In this model, the main goal is to estimate the Euclidean parameter β and to predict the real response variable Y conditionally to X. Our approach is based on sliced inverse regression (SIR) method and optimal quantization in L p - norm . We obtain the convergence of the proposed estimators of β and of the conditional distribution. Simulation studies show the good numerical behavior of the proposed estimators for finite sample size.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2011.08.006