Note on the strong consistency of the least squares estimator in nonlinear regression

Abstract

We consider a nonlinear regression model under standard assumptions on the error distribution, We prove an almost sure convergence of weighted sums with an interesting uniformity, and under very general conditions on the parameter space and the regression function we prove the a.s, boundedness and the strong consistency of the least squares estimator, Here we generalize results of Jennrich (1969) to unbounded parameter spaces