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## Mathematical Statistics

by: Mrs. Triston Collier

47

0

4

# Mathematical Statistics STAT 709

Mrs. Triston Collier
UW
GPA 3.57

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

## Popular in Statistics

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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3IXR3SUOJ p 81 31311311 qu511 111 11 1 u 9 390 39LXH gt03 f M 113113 1VL Z 00 d 9 oc gt 312113 113th a 1 9 d 3IXR3SUOJ p 81 31311311 qu5 111 1 39suo13maadxa 3311111 131 SG1R1XRA umpum umpuadapm aq ZX lX 331 711 maxoaql 39sa1qzz1mA umptm1 pamq1ns1p A 111gt313uap1 KHJRSSGJGU 3011 mq umpuadapm 10 smuanbas 101 s1 31861 3x311 111 1161 8mm 111 1110103111 pm 3171 33131axg 111 punt aq um 0c 1X g 10 68123 113 101 83111331 mung 39pau1mqo aq um a 31mm 108110138 113 110113 oc gt 1X g 11 ptmq 131130 113 no u m XG1dIH1S 11311111 p 11 321 31hmzxg 111 paqs11qmsa K111211331 s1 1 rm pm ng o3 safimAum 1 111 I 113113 oc gt 1Xg 11 391 Xg 4 5311313111118 pamud 113 111013 179 aspwxg 0c gt 1Xg sa11dm1 113111411 lu 12 gt u 2 I Xld Z u 2 I Xld Z 00 00 K1dm1 sf X 110 uo13dmnss 2 39p391391 113 pm 0 N u X 1711 aspwxg 111013 44 9Dlt u 1 u u u u 0 4 e IAMLL I u 21L uX Wm 3921 9 4 611108 101 sp1m1 a 31211 asoddng 395318833311 113 aAmd 3M 3100po 113 111 ImA18 81 5311313111118 101 100m 111 11 39Smngzqmd Hg 0 03 a wwm 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aq pm 01 Xf Xvi g39 ummaql N115 aq SQ gt xpxfi 19f lX g pm 0c gt xpxf19f lXfg ZI maxqu SQ 391 0 uo uopnqmsgp mm un aq Sumpq sqqzzgmx mopmu 39p39g39g aq ZX lX 331 390 xpxf19 3mg Sugmnsszz xpxf10 mg1 0 0 0 00H x1zx1lx L HE G l i it 1113 1 11 I 31219 moqs man a jumsum p s 0 lt 9 awqm 2 up w 155 S xf S 0 SugSjsgws 0 no summing snonunum aq 5 pm f 331 91 aldmexg

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