Parallel Monte Carlo for entropy robust estimation

Abstract

A new method of entropy-robust nonparametric estimation of probability density functions (PDFs) of the characteristics of dynamic randomized models with structured nonlinearities given a small amount of data is proposed. Optimal PDFs are shown to belong to the exponential class with Lagrange multipliers being its parameters. In order to determine these parameters, a system of equations with integral components is constructed. An algorithm for solving this problem is developed based on parallel Monte Carlo techniques. The accuracy of the numerical integration for the given class of integral components and the probability of its achievement are estimated. The method is applied to a second-degree nonlinear dynamic system with the given structure of exponential nonlinearity.