Convergence systems and strong consistency of least squares estimates in regression models

AbstractA recent theorem of T. L. Hai, H. Robbins, and C. Z. Wei (J. Multivariate Anal. 9 (1979), 343–362) is extended to a more general form which unifies previous results in the literature on the strong consistency of least squares estimates in multiple regression models with nonrandom regressors. In particular the issue of strong consistency of the least squares estimate in the Gauss-Markov model, in the i.i.d. model with infinite second moment, and in general time series models is examined. In this connection, some basic properties of convergence systems are also obtained and are applied to the strong consistency problem