STAB57H3 Lecture Notes - Lecture 25: Independent And Identically Distributed Random Variables, Continuous Mapping Theorem, Consistent Estimator
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There are some properties of of an estimator: unbiasedness, consistency, sufficiency, efficiency. Let tn be an estimator of parameter. Tn is said to be consistent(in probability) if tn. In words, tn converges to in probability. If tn then tn is called consistent(almost surely). In this course we will only talk about consistent(in probability) If xi iid ) then x is a consistent estimator of. If xi iid poisson(then x is a consistent estimator of. And we can say this for few other known distributions (do it yourself) We can still use lln but with the help of a well known lemma and the continuous. Yoy xutyu sxty. xn xdtsy sxinp ycoutiuwuse. mn irtorem mapping theorem. Xusx gl be a continuous fun on then guangxi. Note: using continuous mapping theorem, we can say, s is a consistent estimator of . 5 e pwning 5 is a consistent estimator of.
