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Unformatted text preview: STAT 409 Examples for 09/02/2009 Fall 2009 Def An estimator for is said to be consistent if P , i.e., for all > 0, P  as n . The ( Weak ) Law of Large Numbers: Let X 1 , X 2 , be i.i.d. with mean and standard deviation . Let n n n X ... X X 1 + + = , n = 1, 2, . Then X P n . That is, for all > 0, ( 29 X P lim =  n n . 1. If the random variable Y denotes an individuals income, Paretos law claims that P ( Y y ) = y k , where k is the entire populations minimum income. It follows that f Y ( y ) = 1 1 + y k , y k ; 1. Assume k is known. a) Recall that the method of moments estimator ~ of , is k = Y Y ~ . Show that ~ is a consistent estimator of . b) Recall that the maximum likelihood estimator of , is k n n n i i ln 1 Y ln  = = ....
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This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.
 Spring '11
 Stepanov
 Law Of Large Numbers, Standard Deviation

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