Accuracy of reconstruction of the multidimensional probability density by wavelet estimates of one-dimensional projections

The paper considers the problem of non-parametric estimation of a multidimensional probability density. The method of solving this problem is based on the construction of wavelet estimates for one-dimensional projections of the original random vector onto different directions and inversion of the Radon transform. This method of constructing estimates can serve as an alternative to the calculation of kernel density estimates and multivariate wavelet estimates. Wavelet estimates are sensitive to local features of the function being evaluated and therefore are well suited for solving this problem in a situation where the density has a different degree of regularity at different regions. Another important advantage of the considered method is its parallel structure, which makes it possible to significantly accelerate the construction of estimates on computational systems supporting parallel computations. The paper briefly describes the essence of the method and proves statements on the rate of the error decay (in terms of the uniform distance between the estimate and the estimated density function) in the case when the estimated probability density function does not have a compact support.