Weighted uniform consistency of kernel density estimators
نویسندگان
چکیده
منابع مشابه
Weighted Uniform Consistency of Kernel Density Estimators
Let fn denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let (t) be a positive continuous function such that ‖ f β‖∞ < ∞ for some 0 < β < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2| loghn | ‖ (t)(fn(t)−Efn(t))‖∞ to be stochastically bounded and to converge a.s. to a constant are obtained...
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Let fn denote the usual kernel density estimator in several dimensions. It is shown that if {an} is a regular band sequence, K is a bounded square integrable kernel of several variables, satisfying some additional mild conditions ((K1) below), and if the data consist of an i.i.d. sample from a distribution possessing a bounded density f with respect to Lebesgue measure on R, then lim supn→∞ √ n...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2004
ISSN: 0091-1798
DOI: 10.1214/009117904000000063