## The Annals of Probability

### Limit Processes for Sequences of Partial Sums of Regression Residuals

Ian B. MacNeill

#### 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.

#### Article information

Source
Ann. Probab., Volume 6, Number 4 (1978), 695-698.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995491

Digital Object Identifier
doi:10.1214/aop/1176995491

Mathematical Reviews number (MathSciNet)
MR494708

Zentralblatt MATH identifier
0377.60028

JSTOR