Examples of inconsistency of maximum likelihood estimates

Bahadur, R. R. (1958) Examples of inconsistency of maximum likelihood estimates Sankhya, 20 (3-4). pp. 207-210. ISSN 0972-7671

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This note contains two examples, concerning independent observations from a fixed population of real values, where maximum likelihood estimates of the population distribution function do not converge, as the sample size tends to infinity, to the actual distribution function. Such examples are of interest since in previously published examples of the failure of the method, the estimated distribution, if it is exists at all, does converge to the actual one.

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