Transcription of Chapter 2 The Maximum Likelihood Estimator
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Chapter 2 The Maximum Likelihood Estimator
Chapter 2. The Maximum Likelihood Estimator We start this Chapter with a few quirky examples , based on estimators we are already familiar with and then we consider classical Maximum Likelihood estimation. Some examples of estimators Example 1. Let us suppose that {Xi }ni=1 are iid normal random variables with mean and variance 2 . P. The best estimators unbiased estimators of the mean and variance are X = n1 ni=1 Xi P P P 2. and s2 = n 1 1 ni=1 (Xi X )2 respectively. To see why recall that i X i and i Xi P P 2. are the sufficient statistics of the normal distribution and that i Xi and i Xi are complete minimal sufficient statistics.
calculate their joint likelihood. (i) Calculate their sucient statistics. (ii) Propose a class of estimators for µ. 2.2 The Maximum likelihood estimator There are many di↵erent parameter estimation methods. However, if the family of distri-butions from the which the parameter comes from is known, then the maximum likelihood 56
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