What Do Kernel Density Estimators Optimize?

What Do Kernel Density Estimators Optimize?

Some linkages between kernel and penalty methods of density estimation are explored. It is recalled that classical Gaussian kernel density estimation can be viewed as the solution of the heat equation with initial condition given by data. We then observe that there is a direct relationship between the kernel method and a particular penalty method of density estimation. For this penalty method, ...

Deconvoluting Kernel Density Estimators

This paper considers estimation of a continuous bounded probability density when observations from the density are contaminated by additive measurement errors having a known distribution. Properties of the estimator obtained by deconvolving a kernel estimator of the observed data are investigated. When the kernel used is sufficiently smooth the deconvolved estimator is shown to be pointwise con...

Pruning kernel density estimators

Bagging classifiers based on Kernel density estimators

A lot of research is being conducted on combining classification rules (classifiers) to produce a single one, known as an ensemble, which in general is more accurate than the individual classifiers making up the ensemble. Two popular methods for creating ensembles are Bagging introduced by Breiman, (1996) and, AdaBoosting by Freund and Schapire (1996). These methods rely on resampling technique...

Consistency of Robust Kernel Density Estimators

The kernel density estimator (KDE) based on a radial positive-semidefinite kernel may be viewed as a sample mean in a reproducing kernel Hilbert space. This mean can be viewed as the solution of a least squares problem in that space. Replacing the squared loss with a robust loss yields a robust kernel density estimator (RKDE). Previous work has shown that RKDEs are weighted kernel density estim...