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Maximum likelihood

wikipedia.org
The Rao?Blackwell theorem, a result which yields a process for finding the best possible unbiased estimator (in the sense of having minimal mean squared error). The MLE is often a good starting place for the process.
Maximum likelihood - wikipedia.org - Your Highlight Location 326-328 | Added on Monday, 24 June 13 18:00:44
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Maximum a posteriori (MAP) estimator, for a contrast in the way to calculate estimators when prior knowledge is postulated.
Maximum likelihood - wikipedia.org - Your Highlight Location 312-313 | Added on Monday, 24 June 13 17:59:49
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Maximum-likelihood estimation was recommended, analyzed (with flawed attempts at proofs) and vastly popularized by R. A. Fisher between 1912 and 1922 (although it had been used earlier by Gauss, Laplace, T. N. Thiele, and F. Y. Edgeworth). Reviews of the development of maximum likelihood have been provided by a number of authors.
Maximum likelihood - wikipedia.org - Your Highlight Location 300-305 | Added on Monday, 24 June 13 17:59:32
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Much of the theory of maximum-likelihood estimation was first developed for Bayesian statistics, and then simplified by later authors.
Maximum likelihood - wikipedia.org - Your Highlight Location 305-306 | Added on Monday, 24 June 13 17:59:20
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Second-order efficiency after correction for bias.
Maximum likelihood - wikipedia.org - Your Highlight Location 80-80 | Added on Monday, 24 June 13 17:51:02
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Efficiency, i.e., it achieves the Cramér?Rao lower bound when the sample size tends to infinity. This means that no consistent estimator has lower asymptotic mean squared error than the MLE (or other estimators attaining this bound).
Maximum likelihood - wikipedia.org - Your Highlight Location 77-80 | Added on Monday, 24 June 13 17:50:56
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Asymptotic normality: as the sample size increases, the distribution of the MLE tends to the Gaussian distribution with mean and covariance matrix equal to the inverse of the Fisher information matrix.
Maximum likelihood - wikipedia.org - Your Highlight Location 75-77 | Added on Monday, 24 June 13 17:50:35
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Consistency: the sequence of MLEs converges in probability to the value being estimated.
Maximum likelihood - wikipedia.org - Your Highlight Location 74-75 | Added on Monday, 24 June 13 17:50:26
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like other estimation methods, maximum-likelihood estimation possesses a number of attractive limiting properties: As the sample-size increases to infinity, sequences of maximum-likelihood estimators have these properties:
Maximum likelihood - wikipedia.org - Your Highlight Location 71-73 | Added on Monday, 24 June 13 17:50:20
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