A Comparative Study of Nonparametric Kernel estimators with Gaussian Weight Function

Universal consistency of kernel nonparametric M-estimators

We prove that in the case of independent and identically distributed random vectors (Xi, Yi) a class of kernel type M-estimators is universally and strongly consistent for conditional M-functionals. The term universal means that the strong consistency holds for all joint probability distributions of (X, Y ). The conditional M-functional minimizes (2.2) for almost every x. In the case M(y) = |y|...

Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators de...

Nonparametric density deconvolution by weighted kernel estimators

JSM, Denver, 4 August 2008 – 3 / 23 We observe a univariate random sample Y1, . . . , Yn from a density g, where Yi = Xi + Zi (i = 1, . . . , n). Here X1, . . . , Xn are independent and identically distributed with unknown continuous density f , and the measurement errors Z1, . . . , Zn form a random sample from the continuous density η which we assume to be known. Our goal is to obtain a nonpa...

Weighted Kernel Estimators in Nonparametric Binomial Regression

This paper is concerned with nonparametric binomial regression. Two kernel-based binomial regression estimators and their bias-adjusted versions are proposed, whose kernels are weighted by the inverses of variance estimators of the observed proportion at each covariate. Asymptotic theories for deriving asymptotic mean squared errors (AMSEs) of proposed estimators are developed. Comparisons with...

A Comparative Study Of Parametric And Nonparametric Regressions