hw5_stat210a

hw5_stat210a - UC Berkeley Department of Statistics STAT...

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

View Full Document Right Arrow Icon
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 Fall 2006 Issued: Thursday, September 28, 2006 Due: Thursday, October 5, 2006 A useful de±nition for this problem set: Defnition: An equalizer procedure is a rule with constant risk (i.e., R ( θ, δ ) = c for all θ Θ). Problem 5.1 Let Θ = (0 , + ) and A = [0 , ), and suppose that X Poi( θ ). Consider the loss function L ( θ, a ) = ( θ - a ) 2 . (a) Show that the estimator δ ( X ) = X is an equalizer rule. (b) Show that δ is generalized Bayes with respect to the improper prior that is uniform on (0 , ). (c) Find Bayes estimators with respect to the family of Gamma( a, b ) priors. Problem 5.2 For θ (0 , 1), let X Bin( n, θ ), and consider the weighted quadratic loss function L ( θ, a ) = ( θ - a ) 2 θ (1 - θ ) . (Note that this loss function penalizes more severely for extreme values of θ near 0 or 1.) (a) Show that for this loss function, δ
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

hw5_stat210a - UC Berkeley Department of Statistics STAT...

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