Quasi-Monte Carlo Methods for Estimating a Multivariate Regression Function

Quasi-Monte Carlo （QMC） methods are widely used for solving different problems of numerical analysis and statistics, such as integration, optimization, experimental design, simulation of stochastic processes, etc. In this paper, these methods are suggested for estimating a multivariate regression function. It is shown that, in a rather general case, the “uniform design”（respectively, the “representative points design”）, together with standard QMC estimates （respetively,modified QMC estimates （using quasi-random importance sampling）） of Fourier coefficients of a regression function provide an asyinptotically optimal procedure of projection estimation of the regression function.