NONPARAMETRIC DETECTION OF CHANGEPOINTS FOR SEQUENTIALLY OBSERVED DATA

[摘要] Assume that independent data X1n, ..., X(k(n))n are observed sequentially in time, where k(n) < infinity is a finite horizon. Suppose also that there exists theta is-an-element-of (0, 1] such that X1n, ..., X[k(n)theta]n have distribution nu1,n and X[k(n)theta]+1n, ..., X(k(n))n have distribution nu2,n. The distributions and the changepoint theta are unknown. Our aim is to react as soon as possible after the change has taken place. We propose a nonparametric stopping rule which attains a given probability of ''false alarm'' on the one hand and, on the other hand, is less than or equal to k(n)theta + O(square-root k(n)) with probability one.

[发布日期] 1994-07-01

[关键词] SEQUENTIAL DETECTION OF A CHANGEPOINT;WEAK CONVERGENCE OF 2-PARAMETER STOCHASTIC PROCESSES;MARTINGALE MAXIMAL-INEQUALITIES