Geodesic
Parallel Monte Carlo for entropy-robust estimation
Matematičeskoe modelirovanie, Tome 27 (2015) no. 6, pp. 14-32.

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A new method of entropy-robust nonparametric estimation of probability density functions (PDF) is proposed in the paper. Characteristics of dynamic randomized models with structured nonlinearities are estimated under small amount of data. We have shown that optimal PDF are of exponential class, where parameters are Lagrange multipliers. To determine the parameters a system of equations with integral components has been built. We developed an algorithm for solving this problem, based on parallel Monte Carlo techniques. Estimates of solutions’s accuracy for the class of given integral components and probability of its achivement have been obtained. The method was applied to the problem with nonlinear dynamic system with given structured nonlinearity.
Keywords: entropy, robustness, randomized model, structure of exponential nonlinearity, functional entropy-linear programming, Monte Carlo trials, numerical integration, entropy estimation, small amounts of data, graphic processor. 
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Y. S. Popkov; A. Y. Popkov; B. S. Darkhovskiy. Parallel Monte Carlo for entropy-robust estimation. Matematičeskoe modelirovanie, Tome 27 (2015) no. 6, pp. 14-32. http://geodesic.mathdoc.fr/item/MM_2015_27_6_a1/

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