Date of this Version
The Annals of Statistics
If S(x1,x2,⋯,xn) is any function of n variables and if Xi,X̂i,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 X̂i, so Si=S(X1,X2,⋯,X̂i,⋯,Xn). This is applied to sharpen known variance bounds in the long common subsequence problem.
The original and published work is available at: https://projecteuclid.org/euclid.aos/1176349952#abstract
Efron-Stein inequality, variance bounds, tensor product basis, long common subsequences
Steele, J. M. (1986). An Efron-Stein Inequality for Nonsymmetric Statistics. The Annals of Statistics, 14 (2), 753-758. http://dx.doi.org/10.1214/aos/1176349952
Date Posted: 27 November 2017
This document has been peer reviewed.