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Mathematical Statistics

by: Mrs. Triston Collier

Mathematical Statistics STAT 709

Mrs. Triston Collier
GPA 3.57


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This 1 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 36 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 22 December 47 2007 1 U Statistics Example 1 Let X17 7 Xn be a random sample of random variables having nite EX and EXfZ Let M EX1 and EXfl Find a U statistic that is an unbiased estimator of M and derive its variance and asymptotic distribution Example 2 Let XLXZ7 be independent and identically distributed ran dom variables7 m be a positive integer7 and hz17 7 mm be a function on R such that EhX177Xm2 lt 00 and h is symmetric in its m arguments A U statistic with kernel h of order m is de ned as 71 n U 39 39 n I hltXm 7legt7 1S11lt39ltlmS where Zllti1ltmltimltn denotes the summation over the combinations of m distinct elements 239177z39m from 17771 For k 177m7 de ne hkx177xk Eh177k7Xk177Xm and k varhkX177Xk Show that a C1 SCZ S quot39SCm b iij0forjltkandegt07where1 k m7then k m 2 1 varUn O Of ce 1275A M80 1 Phone 262 1577


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