Average run lengths of an optimal method of detecting a change in distribution. (English) Zbl 0632.62080

Pollak, Moshe

Ann. Stat. 15, 749-779 (1987).

The author, Ann. Stat. 13, 206-227 (1985; Zbl 0573.62074), gave a second- order asymptotically optimal solution to the classical change point problem. In the present paper, he dicusses asymptotic operating characteristics of this and related procedures. Asymptotic expressions for the expected stopping times are obtained. A Monte Carlo study made for the normal model with unit variance indicated that the asymptotic expressions are very good approximations, even when the expected sample sizes are small.

Reviewer: S.N.U.A.Kirmani

MSC:

62L10	Sequential statistical analysis
62P30	Applications of statistics in engineering and industry; control charts
60G40	Stopping times; optimal stopping problems; gambling theory
62E20	Asymptotic distribution theory in statistics
65C05	Monte Carlo methods
62L15	Optimal stopping in statistics

Keywords:

average run lengths; asymptotic operating characteristics; Asymptotic expressions; expected stopping times; Monte Carlo study; approximations

Citations:

Zbl 0573.62074