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. We use the given symbol to represent that the distributionalso depends on a parameter , where could be a real-valued unknown parameter or avector of parameters.
Example 1: Suppose that X is a discrete random variable with the following probability ... Example 5 and 6 illustrate one shortcoming of the concept of an MLE. We know that it is irrelevant whether the pdf of the uniform distribution is chosen to be equal to 1= ...
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