A probability density function (PDF) describes the likelihood of different outcomes for a continuous random variable.

The problem of estimating a probability density function has only recently begun to receive attention in the literature. Several authors [Rosenblatt (1956), Whittle (1958), Parzen (1962), and Watson ...

A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates ...