On convergence rate of probability density projective estimate in L₂

The projective estimate of probability density with bounded variation of k-th derivative is considered. The estimate is obtained by means of stochastic regularization method. The authors propose to choose the regularization parameter with the help of omega-square method. The convergence rate of the estimate to true density in the space L₂ is determined. It is supposed that estimated density has bounded support as well as that its k-th derivative exists and has bounded variation on this support. Proposed projective estimator enables to obtain good approximations not only for large, but also for small sample sizes.