A functional central limit theorem for regression models. (English) Zbl 0936.62072

Bischoff, Wolfgang

Ann. Stat. 26, No. 4, 1398-1410 (1998).

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.

Reviewer: Y.Wu (North York)

MSC:

62J05	Linear regression; mixed models
60F17	Functional limit theorems; invariance principles
62K99	Design of statistical experiments
62G20	Asymptotic properties of nonparametric inference

Keywords:

regression residuals; partial sums processes; functional central limit theorem; functions of Brownian motion; change-point problems

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