Optimal pointwise adaptive methods in nonparametric estimation

On pointwise adaptive nonparametric deconvolution

We consider estimating an unknown function f from indirect white noise observations with particular emphasis on the problem of nonparametric deconvolution. Non-parametric estimators that can adapt to unknown smoothness of f are developed. The adaptive estimators are speciied under two sets of assumptions on the kernel of the convolution transform. In particular, kernels having the Fourier trans...

Pointwise adaptive estimation for quantile regression

A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds...

Adaptive pointwise estimation of conditional density function

Optimal Nonparametric Estimation for Semimartingales

This paper extends a result of Godambe on parametric estimation for discrete time stochastic processes to nonparametric estimation for the continuous time case. Following Hasminskii and Ibragimov (1980), the nonparametric problem is formulated as a parametric one but with infinite dimensional parameter. Let { P } be a family of probability measures such that (D,F,P) is complete , (Ft,t~O) is a ...

Optimal Estimation of Derivatives in Nonparametric Regression

We propose a simple framework for estimating derivatives without fitting the regression function in nonparametric regression. Unlike most existing methods that use the symmetric difference quotients, our method is constructed as a linear combination of observations. It is hence very flexible and applicable to both interior and boundary points, including most existing methods as special cases of...