Strong law for the bootstrap |
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Authors: | K.B. Athreya |
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Affiliation: | Department of Mathematics and Statistics, Iowa State University, Ames, IA 50011, U.S.A. |
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Abstract: | Let X1, X2, X3, … be i.i.d. r.v. with E|X1| < ∞, E X1 = μ. Given a realization X = (X1,X2,…) and integers n and m, construct Yn,i, i = 1, 2, …, m as i.i.d. r.v. with conditional distribution for 1 ? j ? n. ( denotes conditional distribution given X). Conditions relating the growth rate of m with n and the moments of X1 are given to ensure the almost sure convergence of toμ. This equation is of some relevance in the theory of Bootstrap as developed by Efron (1979) and Bickel and Freedman (1981). |
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Keywords: | Bootstrap strong law 62E20 62G05 |
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