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Title: Dependence and the dimensionality reduction principle
Authors: Yatracos, Y. 
Keywords: φ-mixing
Additive and multiplicative regression model
Dimensionality reduction
Kolmogorov's entropy
Minimum distance estimation
Nonparametric regression
Projection pursuit
Rates of convergence
Issue Date: 2004
Citation: Yatracos, Y. (2004). Dependence and the dimensionality reduction principle. Annals of the Institute of Statistical Mathematics 56 (2) : 265-277. ScholarBank@NUS Repository.
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.
Source Title: Annals of the Institute of Statistical Mathematics
ISSN: 00203157
Appears in Collections:Staff Publications

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