## Asymptotic Properties of Extremum Estimators

By extremum estimators we mean estimators obtained by either maximizing or minimizing a certain function defined over the parameter space. First, we shall establish conditions for the consistency and the asymptotic normality of extremum estimators (Section 4.1), and second, we shall apply the results to important special cases, namely, the maximum likelihood estimator (Section 4.2) and the nonlinear least squares estimator (Section 4.3).

What we call extremum estimators Huber called M estimators, meaning maximum-likelihood-like estimators. He developed the asymptotic properties in a series of articles (summarized in Huber, 1981). The emphasis here, however, will be different from his...

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