We derive new tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms. These tests have the advantage that they i) do not depend on the ordering of variables in the forecasting model, ii) are applicable to densities of arbitrary...

Let X = (X1,...,Xp) be a stochastic vector having joint density function fX(x) with partitions X1 = (X1,...,Xk) and X2 = (Xk 1,...,Xp). A new method for estimating the conditional density function of X1 given X2 is presented. It is based on locally Gaussian approximations, but simplified in...

Abstract The estimation of stress-strength reliability in a time-dependent context deals with either the stress or strength or both dynamic. The repeated occurrence of stress in random intervals of time induces a change in the distribution of strength over time. In this paper, we study the...