A functional central limit theorem for regression models
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.
scientific article; zbMATH DE number 1359573