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Mathematical Statistics

by: Mrs. Triston Collier

Mathematical Statistics STAT 710

Mrs. Triston Collier
GPA 3.57


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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 710 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/205090/stat-710-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 710 Discussion 15 March 257 2008 1 Neyman Pearson Lemma Example 1 Let f17 fm1 be Borel functions on R that are integrable with respect to a U nite measure V For given constants t1 tm7 let T be the class of Borel functions b from R to 07 1 satisfying 11777 77 and To be the set of 7s in T satisfying Show that if there are constants cl 7 cm such that 7 1 fm 1 gtle1quot39cmfmz W l 0 mile lt 01f196 mm is a member of 70 then 151 maximizes fa fm dy over b E To Show that if 01 2 0 for all 239 then 151 maximizes f bfm dy over b E T 2 UMP Test Example 2 Suppose that the distribution of X is in a family f9 6 E 9 with monotone likelihood ratio in lX7 where YX has a continuous distri bution Consider the hypotheses H0 6 S 60 versus H1 6 gt 607 where 60 E 9 is known Show that the p value of the UMP test is given by P90 Y 2 y7 where y is the observed value of Y and P9 is the probability corresponding 130 f9 Example 3 Let F and G be two known cumulative distribution functions on R and X be a single observation from the cumulative distribution func tion 6Fz 1 7 6Gz7 where 6 E 01 is unknown i Find a UMP test of size a for testing H0 6 S 60 versus H1 6 gt 607 where Of ce 1275A M80 1 Phone 262 1577 TA Yuan Jiang Email jiangy statwiscedu 60 E 071 is known ii Show that the test TAX E a is a UMP test of size a for testing H0 6 S 61 or 6 2 62 versus H1 61 lt 6 lt 627 where 67 E 071 is known7 j1727 and 61 lt 62 Of ce 1275A M80 2 Phone 262 1577


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