Convergence of stochastic empirical measures

R.J. Beran, L. Le Cam and P.W. Millar

Journal of Multivariate Analysis, 1987, vol. 23, issue 1, 159-168

Abstract: Let Pn be a random probability measure on a metric space S. Let P^n be the empirical measure of kn iid random variables, each distributed according to Pn. Our main theorem asserts that if {Pn} converges in distribution, as random probability measures on S, then so does {P^n}. Applications of the result to the study of bootstrap and other stochastic procedures are given.

Keywords: random; probability; measure; stochastic; empirical; measure; bootstrap; triangular; array; convergence; in; distribution (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (7)

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