hw8_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

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 2006 Issued: Thursday, October 26, 2006 Due: Thursday, November 2, 2006 Some useful notation: The p th quantile of a continuous random variable with invertible CDF F is given by x p = F =1 ( p ). Given an i.i.d. set of samples X 1 ,...,X n , let X (1) ,...,X ( n ) denote the associated order statistics. Define for any p (0 , 1), the p th-sample quantile X ( np ) X ( np ) , where for any x R , the notation x denotes the smallest integer greater than or equal to x . Problem 8.1 (Asymptotics of sample quantiles) Keener (Chapter 10) provides one method for an- alyzing the asymptotic behavior of the sample quantitles X ( np ) . In this problem, we de- velop an alternative approach. We begin by analyzing the uniform case. In particular, let U (1) ,...,U ( n ) be the order statistics of a set of n i.i.d. samples from the Uni[0 , 1] distribu- tion. Let E 1 ,...E n +1 be i.i.d. samples from an exponential distribution with mean 1, and set S k = k i =1 E i , for k = 1 ,..., ( n + 1)....
View Full Document

Page1 / 2

hw8_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