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Note on the strong consistency of the least squares estimator in nonlinear regression. (English) Zbl 0678.62067

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.

MSC:

62J02 General nonlinear regression
60F15 Strong limit theorems
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 0193.472
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