stat210a_fall07_hw8

stat210a_fall07_hw8 - UC Berkeley Department of Statistics...

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: UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 8 Fall 2007 Issued: Thursday, October 25 Due: Thursday, November 1 Reading: Keener: Chapter 10, 11, 21.6, B & D: 3.5, 4.4 Problem 8.1 Find variance-stabilizing transformations for the following statistics and estimation problems: (a) The sample mean X n for i.i.d. samples from Ber( ). (Here we want the transformed statistic to have asymptotic variance independent of .) (b) The sample correlation coefficient r = P n i =1 X i Y i P n i =1 X 2 i P n i =1 Y 2 i for i.i.d. samples from the zero-mean bivariate normal with 2 X = 2 Y = 1 and correlation coefficient ( 1 , 1). (Here we want the transformed statistic to have asymptotic variance independent of .) Problem 8.2 Let X 1 ,...,X n be i.i.d. with E [ X i ] = , var( X i ) = 1, and E [( X i ) 4 ] = 4 , and consider the unbiased estimators of 2 defined by 1 ( X ) = 1 n n summationdisplay i =1 X 2 i 1 , and 2 (...
View Full Document

Page1 / 2

stat210a_fall07_hw8 - UC Berkeley Department of Statistics...

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