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\(\hat \theta _n \) 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\(\hat \theta _n \) 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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Yatracos, Y. Dependence and the dimensionality reduction principle. Ann Inst Stat Math 56, 265–277 (2004). https://doi.org/10.1007/BF02530545
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DOI: https://doi.org/10.1007/BF02530545