stat210a_fall07_hw2

stat210a_fall07_hw2 - 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 2 Fall 2007 Issued: Thursday, September 6 Due: Thursday, September 13 Problem 2.1 Suppose that ( X 1 ,X 2 ,...,X n ) is multivariate normal with unknown mean ( μ,...,μ ), where each component has the same mean μ ∈ R and covariance matrix σ 2 I . First, suppose that σ 2 > 0 is known. Show that T = ∑ n i =1 X i is sufficient for the parameterization θ = μ in two ways: (a) using the factorization criterion, and (b) by direct use of the definition of sufficiency. Now suppose that σ 2 > 0 is not known, and the model is parameterized by θ = ( μ,σ 2 ). Find and establish sufficiency of a non-trivial set of sufficient statistics (i.e., not the data itself). Problem 2.2 Consider a family P = { p ( x ; θ ) | θ ∈ Ω } , where p ( x ; θ ) are density functions with common support X ....
View Full Document

This note was uploaded on 10/17/2009 for the course STAT 210a taught by Professor Staff during the Fall '08 term at Berkeley.

Page1 / 2

stat210a_fall07_hw2 - 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