Zk. Zheng et Lp. Wu, THE LIMITING DISTRIBUTION OF A RECURSIVE RESAMPLING PROCEDURE, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 58, 1995, pp. 47-53
Citations number
4
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
A recursive resampling method is discussed in this paper. Let X(1), X(
2), ..., X(n) be i.i.d. random variables with distribution function F
and construct the empirical distribution function F-n. A new sample X(
n+1) is drawn from F-n and the new empirical distribution function ($)
over tilde F-n+1 in the wide sense, is computed from X(1), X(2), ...,
X(n), X(n+1). Then X(n+2) is drawn from ($) over tilde F-n+1 and ($)
over tilde F-n+2 is obtained. In this way, X(n+m) and ($) over tilde F
-n+m are found. It will be proved that ($) over tilde F-n+m converges
to a random variable almost surely as m goes to infinity and the limit
ing distribution is a compound beta distribution. In comparison with t
he usual non-recursive bootstrap, the main advantage of this procedure
is a reduction in unconditional variance.