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# Mathematical Statistics STAT 709

UW

GPA 3.57

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This 4 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 709 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 47 views. For similar materials see /class/205087/stat-709-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.

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Date Created: 09/17/15

TA Yuan Jiang Email jiangy statwiscedu STAT 709 Discussion 15 November 17 2007 1 Basu s Theorem Example 1 Let X1L7 7Xn7 n gt 27 be a random sample of random vari ables having the uniform distribution on the interval 177 where foo lt a lt b lt 00 Show that XM7X1Xn7X17 239 27 quot771717 are independent of X17Xn for any a and b 2 Admissibility and Optimality Example 2 Let X17 7X be iid random variables from a population P E 737 where 73 is a family of distributions with nite mean M and variance 02 Consider the estimation of M under the squared error loss Let T be the class of all possible estimators7 71 be the class of all linear functions in X177Xn7ie7TX chlXi7 with known 016 R7 1727 7717 and i1 72 Q 71 be a subclass of 71 with 01 1 i1 a Show that there is no T optimal rule b Find a Tg optimal rule if X17 7X are independent random vari l 2 l ables hav1ng a common mean M and varXl With known 1172 z 1727 771 c Find a Tg optimal rule if X17 7X are identically distributed but are correlated 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