A uniform weak law of large numbers under π-mixing with application to nonlinear least squares estimation

Abstract  In B ierens (1981) we have derived a uniform weak law of large numbers for stochastically stable processes with respect to a finite-dependent base. In this paper we show that this uniform weak law carries over to stochastically stable processes with respect to a, more general, φ-mixing base. This generalization will be used for relaxing the conditions for weak consistency and asymptotic normality of nonlinear least squares estimators.