Optimal Estimation of Convolution Integrals

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Abstract
Estimators, obtained as linear combinations of distributions from a prescribed reference set, are used to approximate convolution integrals. These linear combinations have non-negative coefficients which sum to unity, and the elements of the reference set have the same first two moments as the convolution integral. Thus, the estimators are distributions that are equal in the second moment sense to the convolution integral. Evaluation of the optimal estimator is based on minimization of objective functions related to moments of the convolution integral and of the distributions in the reference set. It involves only elementary algebraic operations. The optimal estimator is a convenient and generally satisfactory approximation for the convolution integral.

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