Strong law for the bootstrap
Let X1, X2, X3, ... be i.i.d. r.v. with EX1 < [infinity], E X1 = [mu]. 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 P*(Yn,i = Xj) = 1/n for 1 [less-than-or-equals, slant] j [less-than-or-equals, slant] n. (P* 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 (1/m)[Sigma]mi=1 Yn,i to[mu]. This equation is of some relevance in the theory of Bootstrap as developed by Efron (1979) and Bickel and Freedman (1981).
Year of publication: |
1983
|
---|---|
Authors: | Athreya, K. B. |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 1.1983, 3, p. 147-150
|
Publisher: |
Elsevier |
Subject: | Bootstrap strong law |
Saved in:
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