Two-stage change-point estimators in smooth regression models
Two-stage change-point estimators in smooth regression models
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DOI：
10.1016/s0167-7152(96)00197-6
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发表时间：
1997-07-16
影响因子：
0.8
通讯作者：
Song, KS
中科院分区：
文献类型：
--
作者：
Muller, HG;Song, KS
我们考虑一个固定设计回归模型，其中假设回归函数是平滑的，即，Lipschitz连续，除了只有单侧极限且局部不连续的点。我们提出了一个两步估计这个变点的位置，并研究其渐近收敛性质。在第一步中，初始导频估计的变化点和相关的渐近收缩区间，其中包含真正的变化点的概率收敛到1。在第二步中，在这些间隔内最大化取决于变化点的假定位置的加权平均差，并且最大化的自变量然后是最终的变化点估计器。结果表明，在固定跳情形下，该估计量的估计率为O-p（n（-1））.在连续的情况下，估计器达到速率O-p（n（-1）Delta（n）（-2），其中Delta是跳跃大小的序列，在这种情况下假设其收敛到0。对于连续的情况，建立了不变性原理。一系列适当缩放的偏差过程收敛到一个双边布朗运动与三角漂移。
We consider a fixed design regression model where the regression function is assumed to be smooth, i.e., Lipschitz continuous, except for a point when it has only one-sided limits and a local discontinuity occurs. We propose a two-step estimator for the location of this change point and study its asymptotic convergence properties. In a first step, initial pilot estimates of the change point and associated asymptotically shrinking intervals which contain the true change point with probability converging to 1 are obtained. In the second step, a weighted mean difference depending on the assumed location of the change point is maximized within these intervals and the maximizing argument is then the final change point estimator. It is shown that this estimator attains the rate O-p(n(-1)) in the fixed jump case. In the contiguous case, the estimator attains the rate O-p(n(-1)Delta(n)(-2), where Delta, is the sequence of jump sizes which in this case is assumed to converge to 0. For the contiguous case an invariance principle is established. A sequence of appropriately scaled deviation processes is shown to converge to a two-sided Brownian motion with triangular drift.