A note on the convergence analysis of a sparse grid multivariate probability density estimator

With the recent growth in volume and complexity of available data has come a renewed interest in the problem of estimating multivariate probability density functions. However, traditional methods encounter the curse of dimensionality (complexity grows exponentially with dimension). Here we provide an outline of a convergence analysis of a sparse grid based probability density estimation, which supports the use of the method for moderately complex (up to 15 dimensions) data sets, as has already been demonstrated for sparse grid quadrature and interpolation.