homework3_2011 - PROF HONG FALL 2011 ECONOMICS 3190 PROBLEM...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PROF HONG FALL 2011 ECONOMICS 3190 PROBLEM SET #11 1. Suppose ^ & 1 ; ^ & 2 and ^ & 3 are estimators of &; and we know that E ( ^ & 1 ) = E ( ^ & 2 ) = &; E ( ^ & 3 ) 6 = &; var ( ^ & 1 ) = 12 ; var ( ^ & 2 ) = 10 ; and E ( ^ & 3 & & ) 2 = 6 : Which estimator is the best in terms of MSE criterion? 2. Let X 1 ; X 2 ; X 3 ; X 4 be an i.i.d. random sample from a population with ( ; 2 ) : Consider the following two estimators for : ^ 1 = X 1 + 2 X 2 + 3 X 3 + 4 X 4 10 ; ^ 2 = X 1 + 4 X 2 + 4 X 3 + X 4 10 : Which estimator, ^ 1 or ^ 2 ; is more e cient? 3. A random sample, X 1 ; :::; X n ; is taken from an i.i.d. population with ( ; 2 ) : Consider the following estimator of : ^ = 2 n ( n + 1) n X i =1 i X i = 2 n ( n + 1) ( X 1 + 2 X 2 + 3 X 3 + + nX n ) : (a) Show ^ is unbiased for : (b) Which estimator, ^ or & X n ; is more e cient? [ Hint: P n i =1 i = n ( n +1) 2 and P n i =1 i 2 = n ( n +1)(2 n +1) 6 : ] 4. Suppose f X 1 ; X 2 ; :::; X...
View Full Document

This note was uploaded on 11/30/2011 for the course ECON 3190 at Cornell University (Engineering School).

Page1 / 3

homework3_2011 - PROF HONG FALL 2011 ECONOMICS 3190 PROBLEM...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online