Läuter, Henning Note on the strong consistency of the least squares estimator in nonlinear regression. (English) Zbl 0678.62067 Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 89, 153-175 (1987). Summary: 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 R. I. Jennrich [Ann. Math. Statistics 40, 633-643 (1969; Zbl 0193.472)] to unbounded parameter spaces. Cited in 1 Document MSC: 62J02 General nonlinear regression 60F15 Strong limit theorems 62E20 Asymptotic distribution theory in statistics Keywords:strong law of large numbers; limit distribution; almost sure convergence of weighted sums; a.s. boundedness; strong consistency; least squares estimator; unbounded parameter spaces Citations:Zbl 0193.472 PDFBibTeX XMLCite \textit{H. Läuter}, Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 89, 153--175 (1987; Zbl 0678.62067)