STATS 426 Lecture Notes - Lecture 13: Bias Of An Estimator, Taylor Series, Independent And Identically Distributed Random Variables
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Large sample properites of the mle and variance. In this section we study some of the large sample properties of the mle in standard parametric models and how these can be used to construct con dence sets for or a function of . The method of variance stabilizing transformations will also be discussed as a means of obtaining more precise con dence sets. We will see in this section that in the long run mle"s are the best possible estimators in a variety of di erent models. We will stick to models satisfying the restrictions (a1, a2 and. Hence our results will not apply to the uniform distribution (or ones similar to the uniform). Let us throw our minds back to the cramer-rao inequality. But this is equivalent to the assertion that the correlation between t (x) and ln(x, ) is equal to 1 or -1.
