Limiting bias-reduced Amoroso kernel density estimators for non-negative data

Density Estimators for Truncated Dependent Data

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

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(...

Bias Reduction and Elimination with Kernel Estimators

with Kernel Estimators Stephan R. Sain1 De ember 8, 2000 SUMMARY: A great deal of resear h has fo used on improving the bias properties of kernel estimators. One proposal involves removing the restri tion of non-negativity on the kernel to onstru t \higher-order" kernels that eliminate additional terms in the Taylor's series expansion of the bias. This paper onsiders an alternative that uses a ...