Two existing density estimators based on local likelihood have properties that are comparable to those of local likelihood regression but they are much less used than their counterparts in regression. We consider truncation as a natural way of localising parametric density estimation. Based on this idea, a third local likelihood density estimator is introduced. Our main result establishes that ...

I calculate the superfluid density of a nonequilibrium steady state condensate of particles with finite lifetime. Despite the absence of a simple Landau critical velocity, a superfluid response survives, but dissipation reduces the superfluid fraction. I also suggest an idea for how the superfluid density of an example of such a system, i.e., microcavity polaritons, might be measured.

Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it is heavily a↵ected by boundary bias issues. In addition, most common copulas admit unbounded ...

Conditional density estimation. The idea of conditional density estimation is to construct a density estimate f̂(y|x) for a dependent variable y, conditional on a vector of variables x. This can be seen as a generalization of regression, where instead of estimating the expected value E(y|x) alone, we instead model the full density. This is especially important for multi-modal densities, where th...

In statistical pattern recognition, it is important to avoid density estimation since density estimation is often more difficult than pattern recognition itself. Following this idea—known as Vapnik’s principle, a statistical data processing framework that employs the ratio of two probability density functions has been developed recently and is gathering a lot of attention in the machine learnin...