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Inference for Change-Point and Post-Change Mean with Possible Change in Variance

机译：可能存在方差变化的变化点和变化后平均值的推论

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摘要

For a sequence of independent normal random variables, we consider the estimation of the change-point and the post-change mean after a change in the mean is detected by a CUSUM procedure, subject to a possible change in variance. Conditional on the event that a change is detected and it occurred far away from the starting point and the threshold is large, the (absolute) bias of the maximum likelihood estimator for the change-point (obtained at the reference value) is found. The first-order biases for the post-change mean and variance estimators are also obtained by using Wald's Likelihood Ratio Identity and the renewal theorem. In the local case when the reference value and the post-change mean are both small, accurate approximations are derived. A confidence interval for post-change mean based on a corrected normal pivot is then discussed.
机译：对于一系列独立的正常随机变量，我们考虑在CUSUM程序检测到均值变化后，可能会有方差变化的情况下，估计变化点和变化后均值。以检测到变化并且发生在距起点很远且阈值较大的事件为条件，找到变化点的最大似然估计器（在参考值处获得）的（绝对）偏差。变更后均值和方差估计量的一阶偏差也可以通过使用Wald的似然比恒等式和更新定理来获得。在参考值和变化后平均值均较小的局部情况下，可以得出精确的近似值。然后讨论了基于校正后的法线枢轴的变化后平均值的置信区间。

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