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Optimal quantization applied to sliced inverse regression

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Publication Date
Volume
142
Issue
2
Identifiers
DOI: 10.1016/j.jspi.2011.08.006
Keywords
  • Optimal Quantization
  • Semiparametric Regression Model
  • Sliced Inverse Regression (Sir)
  • Reduction Dimension

Abstract

Abstract 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.

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