A functional central limit theorem for regression models

• 成果类型: Article
• 署名作者: Bischoff, W
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1398-1410
• 关键词: unknown times; parameter changes; partial-sums; tests; constancy; RESIDUALS

摘要

Let a linear regression be given. For detecting change-points, it is usual to consider the sequence of partial sums of least squares residuals whence a partial sums process is defined. Given a sequence of exact experimental designs, we consider for each design the corresponding partial sums process. If the sequence of designs converges to a continuous design, we derive the explicit form of the limit process of the corresponding sequence of partial sums processes. This is a complicated function of the Brownian motion. These results are useful for the problem of testing for change of regression at known or unknown times.