In contrast to the analysis of abrupt changes, methods for detecting gradual change points are less developed. In this paper, we are interested in the scenario that the variance of data may vary gradually while the mean of data changes in a smooth fashion. We propose a penalized weighted least squares approach with an iterative estimation procedure to detect the gradual variance change point with a smoothly changing mean function. The null distribution of the test statistic is derived in association with the consistency of estimates. The performance of our method is illustrated by means of a simulation study and a real data example.

中文翻译：

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具有平滑变化的平均趋势的逐步方差变化点检测

与突变的分析相比，用于检测渐变点的方法较少。在本文中，我们对以下情况感兴趣：数据方差可能会逐渐变化，而数据均值会以平滑的方式变化。我们提出了一种带有迭代估计程序的惩罚加权最小二乘方法，以检测具有平滑变化的均值函数的渐进方差变化点。与估计的一致性相关联得出检验统计量的零分布。通过仿真研究和实际数据示例说明了我们方法的性能。