Discrimination distance bounds and statistical applications
Bounds are obtained for the Kullback-Leibler discrimination distance between two random vectors X and Y. If X is a sequence of independent random variables whose densities have similar tail behavior and \(Y=AX\), where A is an invertible matrix, then the bounds are a product of terms depending on A and X separately. These bounds help indicate the best possible rate of convergence for any estimator of the parameters of an auto-regressive process with innovations in the domain of attraction of a stable law. We provide a general theorem establishing the link between total variation proximity of measures and the rate of convergence of statistical estimates to complete our argument.
Kullback-Leibler discrimination distance
scientific article; zbMATH DE number 4122967
scientific article