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Two‐stage model selection procedures in partially linear regression
Author(s) -
Bunea Florentina,
Wegkamp Marten H.
Publication year - 2004
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315936
Subject(s) - minimax , mathematical proof , mathematics , stage (stratigraphy) , oracle , linear regression , model selection , least squares function approximation , linear model , estimation , selection (genetic algorithm) , regression , mathematical optimization , computer science , statistics , estimator , artificial intelligence , economics , geology , geometry , paleontology , software engineering , management
The authors propose a two‐stage estimation procedure for the partially linear model Y = f o (T) + X'β o + ψ. They show how to estimate consistently the location of the nonzero components of β o . Their approach turns out to be compatible with minimax adaptive estimation of f o over Besov balls in the case of penalized least squares. Their proofs are based on a new type of oracle inequality.