Strong consistency of least squares estimates in multiple regression models with random regressors

摘要

The strong consistency of the least squares estimator in multiple regression models is established assuming the randomness of the regressors and errors with infinite variance. Only moderately restrictive conditions are imposed on the stochastic model matrix and the errors will be random variables having moment of order r, 1 ≤ r ≤ 2. In our treatment, we use Etemadi's strong law of large numbers and a sharp almost sure convergence for randomly weighted sums of random elements. Both techniques permit us to extend the results of some previous papers.