## The Annals of Probability

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 62J05: Linear regression

**Keywords**

Brownian motion harmonic regression polynomial regression regression residuals weak convergence

#### Citation

MacNeill, Ian B. Limit Processes for Sequences of Partial Sums of Regression Residuals. Ann. Probab. 6 (1978), no. 4, 695--698. doi:10.1214/aop/1176995491. https://projecteuclid.org/euclid.aop/1176995491