RECONSTRUCTIONS OF PIECEWISE CONTINUOUS AND DISCRETE FUNCTIONS USING MOMENTS

The problem of recovering a moment-determinate multivariate function f via its moment sequence is studied. Under mild conditions on f, the point-wise and \(L_1\) $L_1$ -rates of convergence for the proposed constructions are established. Two cases where f is the uniform density function defined on a compact set, and f is a discrete probability mass function are investigated. Calculations of the approximants and simulation studies illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of the proposed approximations are recorded in Tables 1–5.