Dependence and the dimensionality reduction principle |
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| Authors: | Yannis Yatracos |
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| Affiliation: | (1) Department of Statistics and Applied Probability, The National University of Singapore, 6 Science Drive 2, 117546 Singapore, Singapore |
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| 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  is proposed for a smooth projection pursuit regression-type function θ∈Я, that is either additive or multiplicative, in the presence of or without interactions. Upper bounds on theL 1-risk and theL 1-error of  are obtained, under restrictions on the order of decay of the mixing coefficient. The bounds show explicitly the addive effect of ϕ-mixing on the error, and confirm the dimensionality reduction principle. |
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| Keywords: | Additive and multiplicative regression model dimensionality reduction projection pursuit Kolmogorov’ s entropy minimum distance estimation nonparametric regression ϕ -mixing rates of convergence |
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