Transcription of Maximum Likelihood Estimation 1 Maximum Likelihood …
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Maximum Likelihood Estimation 1 Maximum Likelihood …
Math 541: Statistical Theory IIMaximum Likelihood EstimationLecturer: Songfeng Zheng1 Maximum Likelihood EstimationMaximum Likelihood is a relatively simple method of constructing an estimator for an un-known parameter . It was introduced by R. A. Fisher, a great English mathematical statis-tician, in 1912. Maximum Likelihood Estimation (MLE) can be applied in most problems, ithas a strong intuitive appeal, and often yields a reasonable estimator of . Furthermore, ifthe sample is large, the method will yield an excellent estimator of . For these reasons, themethod of Maximum Likelihood is probably the most widely used method of Estimation that the random variablesX1, , Xnform a random sample from a distributionf(x| ); ifXis continuous random variable,f(x| ) is pdf, ifXis discrete random variable,f(x| ) is point mass function.
The meaning of maximum likelihood is as follows. We choose the parameter that makes the likelihood of having the obtained data at hand maximum. With discrete distributions, the likelihood is the same as the probability. We choose the parameter for the density that maximizes the …
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