#actuarialfact
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trishladeep20
A fun actuarial fact. Widespread use of maximum likelihood rose between 1912 and 1922 when Ronald Fisher recommended, widely popularized, and carefully analyzed maximum-likelihood estimation (with fruitless attempts at proofs).
Maximum-likelihood estimation finally transcended heuristic justification in a proof published by Samuel S. Wilks in 1938, now called Wilks’ theorem. The theorem shows that the error in the logarithm of likelihood values for estimates from multiple independent observations is asymptotically χ 2-distributed, which enables convenient determination of a confidence region around any estimate of the parameters. The only difficult part of Wilks’ proof depends on the expected value of the Fisher information matrix, which is provided by a theorem proven by Fisher. Wilks continued to improve on the generality of the theorem throughout his life, with his most general proof published in 1962.
Reviews of the development of maximum likelihood estimation have been provided by a number of authors.
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