Splynes in nonparametric density estimation

A distribution density is obtained by the maximum likelihood method in the range of densities with a modulo-constrained $n$-th derivative of the density logarithm. The estimate logarithm is shown to be an $n$-th order splyne and the rate of convergence is estimated. With $n$=1 the Monte-Carlo technique estimates the goodness of the estimate and of the Parsen density estimate.