Local multiplicative bias correction for asymmetric kernel density estimators

Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval

We consider kernel-type methods for estimation of a density on [0, 1] which eschew explicit boundary correction. Our starting point is the successful implementation of beta kernel density estimators of Chen (1999). We propose and investigate two alternatives. For the first, we reverse the roles of estimation point x and datapoint Xi in each summand of the estimator. For the second, we provide k...

Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution∗

Masry (1996b) provides estimation bias and variance expression for a general local polynomial kernel estimator in a general multivariate regression framework. Under smoother conditions on the unknown regression and by including more refined approximation terms than that in Masry (1996b), we extend the result of Masry (1996b) to obtain explicit leading bias terms for the whole vector of the loca...

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 Normality for Deconvolving Kernel Density Estimators

Suppose that we have 11 observations from the convolution model Y = X + £, where X and £ are the independent unobservable random variables, and £ is measurement error with a known distribution. We will discuss the asymptotic normality for deconvolving kernel density estimators of the unknown density f x 0 of X by assuming either the tail of the characteristic function of £ behaves as II I~Oexp(...