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Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. (English) Zbl 0639.62020
The purpose of this article is to derive large sample properties of the likelihood surface under conditions similar to H. CramĂ©r’s [see Skand. Aktuarietidskr. 29, 85-94 (1946; Zbl 0060.305)], but allowing the true parameter value to be on the boundary of the parameter space. The results are stated in terms of properties of maximum likelihood estimators in the loose sense. By analogy to G. Kulldorf [see ibid. 1957, 129-144 (1958; Zbl 0084.149)], the authors define any point in the parameter space at which a local maximum of the likelihood function occurs to be a maximum likelihood estimator in the loose sense.
The results presented include the existence of a consistent maximum likelihood estimator, the large sample distribution of that estimator, and the large sample distribution of likelihood ratio statistics.
Reviewer: V.Olman

MSC:
62F12 Asymptotic properties of parametric estimators
62A01 Foundations and philosophical topics in statistics
62F05 Asymptotic properties of parametric tests
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