Abstract
The mean-square error minimization of the global histogram-type error estimate of the Monte Carlo method is performed. In the special case, the simulation of a Markov chain with transitional density proportional to the product of the absolute value of the original kernel and the averaging weight is optimal. In the general case, the transitional density minimizing the weighted sum of the variances of several functionals is basic. A sufficiently simple approximation to the asymptotic variant of such density is obtained. The minimax variant of the algorithm is also considered.
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