Lecture 18-2007 - Mean Squared Error and Maximum Likelihood...

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Mean Squared Error and Maximum Likelihood Lecture XVIII I. Mean Squared Error A. As stated in our discussion on closeness, one potential measure for the goodness of an estimator is 2 ˆ E where ˆ is the estimator and is the true value. B. In the preceding example, the mean square error of the estimate can be written as: 2 ET where is the true parameter value between zero and one. C. This expected value is conditioned on the probability of T at each level value of . For example, if 0 then the probability of each X becomes: 1 ,1 X X PX If the two events are independent: 1 12 , , 1 XX P X X The mean squared error at any theta can then be derived as 2 2 2 0,0, 0 2 0,1, .5 1,1, 1 MSE P P P D. The mean square error for S can similarly be computed as: 22 0, 0 1, 1 MSE P P E. Finally, the mean square error of W can be written as 2 (.5 ) MSE F. The mean square errors for each estimator can then be depicted as:
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AEB 6933–Mathematical Statistics for Food and Resource Economics Lecture XVIII Professor Charles Moss Fall 2007 2 G. Definition 7.2.1. Let X and Y be two estimators of . We say that X is better (or more efficient) than Y if 22 E X E Y for all and strictly less than for at least one .
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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Lecture 18-2007 - Mean Squared Error and Maximum Likelihood...

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