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Title: Dependence and the dimensionality reduction principle
Authors: Yatracos, Yannis G. 
Keywords: Mathematical models
Parameter estimation
Statistical methods
Problem solving
Issue Date: 2004
Publisher: Springer Link
Source: Annals of the Institute of Statistical Mathematics, 2004, Volume 56, Issue 2, Pages 265-277
Abstract: Stone's dimensionality reduction principle has been confirmed on several occasions for independent observations. When dependence is expressed with φ-mixing, a minimum distance estimate θ̂n is proposed for a smooth projection pursuit regression-type function θ ∈, that is either additive or multiplicative, in the presence of or without interactions. Upper bounds on the L1-risk and the L 1-error of θ̂n are obtained, under restrictions on the order of decay of the mixing coefficient. The bounds show explicitly the additive effect of φ-mixing on the error, and confirm the dimensionality reduction principle.
ISSN: 0020-3157 (print)
1572-9052 (online)
DOI: 10.1007/BF02530545
Rights: © 2004 The Institute of Statistical Mathematics
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