hw10_stat210a

# hw10_stat210a - UC Berkeley Department of Statistics STAT...

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

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

View Full Document
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 10 Fall 2006 Issued: Thursday, November 9, 2006 Due: Thursday, November 16, 2006 Problem 10.1 (A non-parametric hypothesis test) A set of i.i.d. samples Y 1 ,...,Y n is drawn from an unknown distribution F . The null hypothesis H asserts that F has median μ = μ , while the alternative H 1 asserts that μ > μ . (Note that both hypotheses are composite, but neither is based on a parametric model, since only μ is given while the form of F is unknown.) (a) Consider the statistic S = ∑ n i =1 I [ Y i > μ ]. Compute the exact distribution of S under the null hypothesis. How could this be useful in performing a hypothesis test? (b) Consider the test δ s ( Y ) that rejects H when S exceeds some threshold s . Use asymp- totic theory to approximate the level α ( s ) = E [ δ s ( Y )] of this test under H as a function of s . (This test is known as a non-parametric sign test .) Problem 10.2Problem 10....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

hw10_stat210a - UC Berkeley Department of Statistics STAT...

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

View Full Document
Ask a homework question - tutors are online