Adaptive Warped Kernel Estimators

Adaptive warped kernel estimators

In this work, we develop a method of adaptive nonparametric estimation, based on "warped" kernels. The aim is to estimate a real-valued function s from a sample of random couples (X,Y ). We deal with transformed data (Φ(X), Y ), with Φ a one-to-one function, to build a collection of kernel estimators. The data-driven bandwidth selection is done with a method inspired by Goldenshluger and Lepski...

On the Adaptive Nadaraya-watson Kernel Regression Estimators

Nonparametric kernel estimators are widely used in many research areas of statistics. An important nonparametric kernel estimator of a regression function is the Nadaraya-Watson kernel regression estimator which is often obtained by using a fixed bandwidth. However, the adaptive kernel estimators with varying bandwidths are specially used to estimate density of the long-tailed and multi-mod dis...

Simple Kernel Estimators for

We consider deconvolution problems where the observations are equal in distribution to Here the random variables in the sums are independent, the E i are exponentially distributed, the L i are Laplace distributed and Y has an unknown distribution F which we want to estimate. The constants i or i are given. These problems include exponential, gamma and Laplace deconvolution. We derive inversion ...

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