This paper by Robert I. Jennrich from the University of California, Los Angeles, focuses on the asymptotic properties of least squares estimators for non-linear parameters. The author establishes conditions for the consistency and asymptotic normality of these estimators and demonstrates that the Gauss-Newton iteration method is asymptotically numerically stable. The paper begins with an introduction to the problem, defining the least squares estimate and discussing the assumptions under which these estimators are valid. It then delves into the theoretical foundations, including the concept of tail products and random samples, and presents several theorems that rigorously prove the asymptotic properties of the estimators. The Gauss-Newton iteration method is shown to be numerically stable under certain conditions, and the paper concludes with examples to illustrate the theoretical results.This paper by Robert I. Jennrich from the University of California, Los Angeles, focuses on the asymptotic properties of least squares estimators for non-linear parameters. The author establishes conditions for the consistency and asymptotic normality of these estimators and demonstrates that the Gauss-Newton iteration method is asymptotically numerically stable. The paper begins with an introduction to the problem, defining the least squares estimate and discussing the assumptions under which these estimators are valid. It then delves into the theoretical foundations, including the concept of tail products and random samples, and presents several theorems that rigorously prove the asymptotic properties of the estimators. The Gauss-Newton iteration method is shown to be numerically stable under certain conditions, and the paper concludes with examples to illustrate the theoretical results.