A self-improvement to the Cauchy–Schwarz inequality

Stephen G. Walker

Statistics & Probability Letters, 2017, vol. 122, issue C, 86-89

Abstract: We present a self improvement to the Cauchy–Schwarz inequality, which in the probability case yields [E(XY)]2≤E(X2)E(Y2)−(|E(X)|Var(Y)−|E(Y)|Var(X))2. It is to be noted that the additional term to the inequality only involves the marginal first two moments for X and Y, and not any joint property. We also provide the discrete improvement to the inequality.

Keywords: Cauchy–Schwarz; Cramer–Rao inequality; Wasserstein distance (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.11.001

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