Dependence and the Dimensionality Reduction Principle
نویسنده
چکیده
Stone's dimensionality reduction principle has been confirmed on several occasions for independent observations. When dependence is expressed with C-mixing, a minimum distance es t imate ~n is proposed for a smooth projection pursuit regression-type function t~ C e, that is either additive or multiplicative, in the presence of or without interactions. Upper bounds on the Ll-risk and the Ll-error of 0,~ are obtained, under restrictions on the order of decay of the mixing coefficient. The bounds show explicitly the additive effect of C-mixing on the error, and confirm the dimensionality reduction principle.
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