The maximal variance of Lipschitz functions (with respect to the ℓ 1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of ...

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 ...

Nonparametric methods provide a flexible framework for estimating the probability density function of random variables without imposing a strict parametric model. By relying directly on observed ...