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August 1998 A functional central limit theorem for regression models
Wolfgang Bischoff
Ann. Statist. 26(4): 1398-1410 (August 1998). DOI: 10.1214/aos/1024691248


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.


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Wolfgang Bischoff. "A functional central limit theorem for regression models." Ann. Statist. 26 (4) 1398 - 1410, August 1998.


Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0936.62072
MathSciNet: MR1647677
Digital Object Identifier: 10.1214/aos/1024691248

Primary: 60F17, 60G15, 62J05

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • August 1998
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