Transcription of Maximum Likelihood Estimation
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Maximum Likelihood Estimation
Topic 15. Maximum Likelihood Estimation Introduction The principle of Maximum Likelihood is relatively straightforward to state. As before, we begin with observations X = (X1 , .. , Xn ) of random variables chosen according to one of a family of probabilities P . In addition, f (x| ), x = (x1 , .. , xn ) will be used to denote the density function for the data when is the true state of nature. Then, the principle of Maximum Likelihood yields a choice of the estimator as the value for the parameter that makes the observed data most probable. Definition The Likelihood function is the density function regarded as a function of . L( |x) = f (x| ), 2 . ( ). The Maximum Likelihood estimate (MLE), . (x) = arg max L( |x). ( ).. Thus, we are presuming that a unique global Maximum exists. We will learn that especially for large samples, the Maximum Likelihood estimators have many desirable properties.
Topic 15 Maximum Likelihood Estimation 15.1 Introduction The principle of maximum likelihood is relatively straightforward to state. As before, we begin with observations ... Maximum likelihood estimation can be applied to a vector valued parameter. For a simplerandom sample of n normal randomvariables ...
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