Minimax properties of Dirichlet kernel density estimators

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

Asymptotic properties of parallel Bayesian kernel density estimators

In this article we perform an asymptotic analysis of Bayesian parallel kernel density estimators introduced by Neiswanger, Wang and Xing [19]. We derive the asymptotic expansion of the mean integrated squared error for the full data posterior estimator and investigate the properties of asymptotically optimal bandwidth parameters. Our analysis demonstrates that partitioning data into subsets req...

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...

Weighted Uniform Consistency of Kernel Density Estimators

Let fn denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let (t) be a positive continuous function such that ‖ f β‖∞ < ∞ for some 0 < β < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2| loghn | ‖ (t)(fn(t)−Efn(t))‖∞ to be stochastically bounded and to converge a.s. to a constant are obtained...