## The Annals of Statistics

### Strong Consistency of Least Squares Estimators in Linear Regression Models

#### Abstract

For the linear regression model $y = X \beta + u$ with stochastic regressor matrix, strong consistency of the least squares estimator of $\beta$ is proved in the case of martingale difference errors and predetermined regressors and for the case where errors and regressors are orthogonal up to the second order. The results obtained are applied to parameter estimation in autoregressive processes, leading to strong consistency if the errors are quasi-independent up to the fourth order.

#### Article information

Source
Ann. Statist., Volume 8, Number 4 (1980), 778-788.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345070

Digital Object Identifier
doi:10.1214/aos/1176345070

Mathematical Reviews number (MathSciNet)
MR572621

Zentralblatt MATH identifier
0468.62060

JSTOR