Steele, J Michael2023-05-232023-05-231986-03-012017-08-24https://repository.upenn.edu/handle/20.500.14332/47682If 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#abstractEfron-Stein inequalityvariance boundstensor product basislong common subsequencesPhysical Sciences and MathematicsArticle