On Upper and Lower Bounds for the Variance of a Function of a Random Variable
On Upper and Lower Bounds for the Variance of a Function of a Random Variable
Chernoff (1981) obtained an upper bound for the variance of a function of a standard normal random variable, using Hermite polynomials. Chen (1980) gave a different proof, using the Cauchy-Schwarz inequality, and extended the inequality to the case of a multivariate normal. Here it is shown how similar upper bounds …