DETECTING RELEVANT CHANGES IN THE MEAN OF NONSTATIONARY PROCESSES-A MASS EXCESS APPROACH

• 成果类型: Article
• 署名作者: Dette, Holger; Wu, Weichi
• 署名单位: Ruhr University Bochum; Ruhr University Bochum; Tsinghua University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1811
• 发表日期: 2019
• 页码: 3578-3608
• 关键词: structural-change; contour clusters; linear-models; regression; inference; tests; quantile; estimator; point

摘要

This paper considers the problem of testing if a sequence of means (mu(t))(t=1, ...,n) of a nonstationary time series (X-t)(t=1, )(...,n) is stable in the sense that the difference of the means mu(1) and mu(t )between the initial time t = 1 and any other time is smaller than a given threshold, that is vertical bar mu(1) - mu(t)vertical bar <= c for all t = 1, ..., n. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location of the roots of the equation vertical bar mu(1) - mu(t)vertical bar = c a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a nonstationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.