Maximizing the expected range from dependent observations under mean-variance information

In this article we derive the best possible upper bound for $E[\max{X_i}-\min_i{X_i}]$ under given means and variances on $n$ random variables $X_i$. The random vector $(X_1,...,X_n)$ is allowed to have any dependence structure, provided $E X_i=μ_i$ and $Var X_i=σ_i^2$, $0<σ_i<\infty$. We provide an explicit characterization of the $n$-variate distributions that attain the equality (extremal random vectors), and the tight bound is compared to other existing results. Key words and phrases: Range; Dependent Observations; Tight Expectation Bounds; Extremal Random Vectors; Probability Matrices; Characterizations.

No reviews yet.

No comments yet.