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 ...

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 ...

Kernel Density Estimation (KDE): A nonparametric method to estimate the probability density function of a random variable by averaging over locally weighted contributions of each data point.

Continuity or discontinuity of probability density functions of data often plays a fundamental role in empirical economic analysis. For example, for identification and inference of causal effects in ...