Variance bounds by a generalization of the Cauchy-Schwarz inequality
type: Item
instance of: scholarly article
title: Variance bounds by a generalization of the Cauchy-Schwarz inequality
zbMATH Open document ID: 0664.60024
DOI: 10.1016/0167-7152(88)90084-3
author: S. H. Smith
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
review text: General upper and lower bounds for Var[g(X)] are obtained, where X is a continuous random variable and g(x), \(x\in (-\infty,\infty)\), is a real- valued function with continuous derivatives of order \(2m+3\). The upper bound depends on \(2m+2\) derivatives of g. The result is a generalization of results of \textit{H. Chernoff} [Ann. Probab. 9, 533-535 (1981; Zbl 0457.60014)] and \textit{T. Cacoullos} [ibid. 10, 799-809 (1982; Zbl 0492.60021)].
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 4086640
zbMATH Keywords: variance bounds
zbMATH Keywords: upper and lower bounds
MaRDI profile type: Publication
full work available at URL: 0167-7152(88)90084-3
OpenAlex ID: W2049266219
cites work: On upper and lower bounds for the variance of a function of a random variable
cites work: On upper bounds for the variance of functions of random variables
cites work: An inequality for the multivariate normal distribution
cites work: A note on an inequality involving the normal distribution
cites work: Eine Bemerkung zur Schwarzschen Ungleichheit
description: scientific article; zbMATH DE number 4086640