Statistics Papers

Document Type

Journal Article

Date of this Version

3-1986

Publication Source

The Annals of Statistics

Volume

14

Issue

2

Start Page

753

Last Page

758

DOI

10.1214/aos/1176349952

Abstract

If S(x1,x2,⋯,xn) is any function of n variables and if Xi,i,1 ≤ i ≤ n are 2n i.i.d. random variables then varS ≤ ½ E i=1n (S - Si)2 where S = S (X1,X2,⋯,Xn) and Si is given by replacing the ith observation with i, so Si=S(X1,X2,⋯,X̂i,⋯,Xn). This is applied to sharpen known variance bounds in the long common subsequence problem.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aos/1176349952#abstract

Comments

At the time of publication, author J. Michael Steele was affiliated with Princeton University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

Keywords

Efron-Stein inequality, variance bounds, tensor product basis, long common subsequences

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Date Posted: 27 November 2017

This document has been peer reviewed.