In:
Australian & New Zealand Journal of Statistics, Wiley, Vol. 44, No. 1 ( 2002-03), p. 109-119
Abstract:
In sequential analysis it is often necessary to determine the distributions of √t Y t and/or √a Y t , where t is a stopping time of the form t = inf{ n ≥ 1 : n+S n +ξ n 〉 a }, Y n is the sample mean of n independent and identically distributed random variables (iidrvs) Y i with mean zero and variance one, S n is the partial sum of iidrvs X i with mean zero and a positive finite variance, and { ξ n } is a sequence of random variables that converges in distribution to a random variable ξ as n →∞ and ξ n is independent of ( X n+1 , Y n+1 ), (X n+2 , Y n+2 ), . . . for all n ≥ 1. Anscombe’s (1952) central limit theorem asserts that both √t Y t and √a Y t are asymptotically normal for large a , but a normal approximation is not accurate enough for many applications. Refined approximations are available only for a few special cases of the general setting above and are often very complex. This paper provides some simple Edgeworth approximations that are numerically satisfactory for the problems it considers.
Type of Medium:
Online Resource
ISSN:
1369-1473
,
1467-842X
DOI:
10.1111/anzs.2002.44.issue-1
DOI:
10.1111/1467-842X.00212
Language:
English
Publisher:
Wiley
Publication Date:
2002
detail.hit.zdb_id:
1468031-2
