A functional central limit theorem for regression models
type: Item
instance of: scholarly article
title: A functional central limit theorem for regression models
zbMATH Open document ID: 0936.62072
author: Wolfgang Bischoff
published in: The Annals of Statistics
publication date: 1999-11-09T00:00:00Z
review text: In a problem of detecting change-points in a linear regression model, 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, the corresponding partial sums process for each design is considered. Assume that the sequence of designs converges to a continuous design. The author derives the explicit form of the limit process of the corresponding sequence of partial sums processes, which is represented as a complicated function of a Brownian motion. These results are useful for the problem of testing for change in regression at known or unknown times.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62K99
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 1359573
zbMATH Keywords: regression residuals
zbMATH Keywords: partial sums processes
zbMATH Keywords: functional central limit theorem
zbMATH Keywords: functions of Brownian motion
zbMATH Keywords: change-point problems
reviewed by: Yuehua Wu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1024691248
OpenAlex ID: W1982629204
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DOI: 10.1214/AOS/1024691248
description: scientific article; zbMATH DE number 1359573