NotesNov19 - • Maximum likelihood estimator may or may...

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Unformatted text preview: • Maximum likelihood estimator may or may not be unbiased. The bias, if present, be- comes small as the sample size increases. • Maximum likelihood estimators are consis- tent, and for large sample sizes their MSE is the smallest possible. • If ˆ θ is the MLE of an unknown parameter θ , and h is a one-to-one function, then h ( ˆ θ ) is a MLE of h ( θ ). Estimation by the method of moments • The moments of the distribution of the sample (the population moments) depend on the unknown parameters. • One can estimate these moments from the sample, resulting in the sample moments. • Equate populations moments and the sam- ple moments, and solve the resulting sys- tem of equations for the unknown param- eters • The solution is a moment estimator of the parameters. Sample moments : Given a sample X 1 ,...,X n , the k th sample mo- ment is ˆ m k = 1 n n X i =1 X k i , k = 1 , 2 ,.......
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This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell.

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NotesNov19 - • Maximum likelihood estimator may or may...

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