stat610hw2 - independent of the minimal sucient statistic...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Statistics 610: Homework 2 (1) Keener’s notes Chapter 3: 11, 15, 19, 20, 31, 32. Chapter 4: 17, 19, 22, 23, 25, 30. (2) Consider X 1 ,X 2 ,...,X n i.i.d. f a,b ( x ) = (1 /b ) e - ( x - a ) /b 1( x > a ). This is called the E ( a,b ) family of distributions, with a R ,b > 0. (a)Show that ( X (1) , n i =1 ( X i - X (1) )) are minimal sufficient when both a,b are unknown. (b)Show also that X (1) is independent of n i =1 ( X i - X (1) ) and determine the distributions of these two statistics. (c) Show that the ratios Z i = ( X ( n ) - X ( i ) ) / ( X ( n ) - X ( n - 1) ) ,i = 1 , 2 ,..., ( n - 2) are
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: independent of the minimal sucient statistic in (a). (3) (a) Let ( X 1 ,X 2 ,...,X n ) be i.i.d. U ( -1 / 2 , + 1 / 2). Show that ( X (1) ,X ( n ) ) is minimal sucient but not complete. (Hint: What happens to the distribution of X ( n )-X (1) ?) (b) Consider ( X 1 ,X 2 ,...,X n ) i.i.d. N ( , 2 ). Show that ( n i =1 X i , n i =1 ( X i-X ) 2 ) is minimal sucient but not complete. 1...
View Full Document

Ask a homework question - tutors are online