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August, 1978 Limit Processes for Sequences of Partial Sums of Regression Residuals
Ian B. MacNeill
Ann. Probab. 6(4): 695-698 (August, 1978). DOI: 10.1214/aop/1176995491

Abstract

Linear regression of a random variable against several functions of time is considered. Limit processes are obtained for the sequences of partial sums of residuals. The limit processes, which are functions of Brownian motion, have covariance kernels of the form: $$K(s, t) = \min (s,t) - \int^t_0 \int^s_0 g(x, y) dx dy.$$ The limit process and its covariance kernel are explicitly stated for each of polynomial and harmonic regression.

Citation

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Ian B. MacNeill. "Limit Processes for Sequences of Partial Sums of Regression Residuals." Ann. Probab. 6 (4) 695 - 698, August, 1978. https://doi.org/10.1214/aop/1176995491

Information

Published: August, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0377.60028
MathSciNet: MR494708
Digital Object Identifier: 10.1214/aop/1176995491

Subjects:
Primary: 60F05
Secondary: 62J05

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • August, 1978
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