Sequential change-point detection when unknown parameters are present in the pre-change distribution
Sequential change-point detection when unknown parameters are present in the pre-change distribution
复制标题
DOI：
10.1214/009053605000000859
复制
发表时间：
2006-02-01
影响因子：
4.5
通讯作者：
Mei, YJ
中科院分区：
文献类型：
--
作者：
Mei, YJ
在顺序变化点检测文献中，大多数研究指定了给定的变化前分布f（θ）处所需的虚警频率，并试图最小化每个可能的变化后分布g（λ）的检测延迟。在本文中，由一些实际的例子，我们首先考虑相反的问题，指定所需的检测延迟在一个给定的变化后的分布，并试图尽量减少每一个可能的变化前的分布f（θ）的误报频率。我们提出了渐近最优的单参数指数族的程序。接下来，我们发展了一个一般理论的变点问题时，变化前的分布f（θ）和变化后的分布g涉及未知参数。我们还将我们的方法应用于检测独立正常观测值均值变化的特殊情况。
In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution f(theta) and tries to minimize the detection delay for every possible post-change distribution g(lambda). In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every possible pre-change distribution f(theta). We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the prechange distribution f(theta) and the post-change distribution g; involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.