Locating a Changed Segment in a Sequence of Bernoulli Variables
研究了在独立伯努利变量序列中，当两个变化点之间的距离已知时，如何定位一个变化片段。推导了检验是否存在变化片段的似然比统计量的分布，以及变化片段位置的最大似然估计量的分布，并给出了长度不超过20的变化片段的数值结果和计算方法。
The theory underlying inferences about a single change point in a sequence of independent Bernoulli variables is extended to the two change points problem where the distance between the two change points is known, namely a changed segment. Both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations. The distribution of the maximum likelihood estimator of the location of the changed segment is derived. Some numerical results for changed segments of length up to 20 are given and computational methods are presented.