Probability density function is a statistical expression defining the likelihood of a series of outcomes for a continuous variable, such as a stock or ETF return.

Asymptotic properties of estimates of a probability density function and its derivatives which use the kernel-method are studied. Some results on the rate of convergence of these estimates are ...

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 ...