Adaptive estimation in the functional nonparametric regression model

Adaptive estimation in the functional nonparametric regression model

In this paper, we consider nonparametric regression estimation when the predictor is a functional random variable (typically a curve) and the response is scalar. Starting from a classical collection of kernel estimates, the bias-variance decomposition of a pointwise risk is investigated to understand what can be expected at best from adaptive estimation. We propose a fully data-driven local ban...

Nonparametric Regression Estimation under Kernel Polynomial Model for Unstructured Data

The nonparametric estimation(NE) of kernel polynomial regression (KPR) model is a powerful tool to visually depict the effect of covariates on response variable, when there exist unstructured and heterogeneous data. In this paper we introduce KPR model that is the mixture of nonparametric regression models with bootstrap algorithm, which is considered in a heterogeneous and unstructured framewo...

On Spatial Adaptive Estimation of Nonparametric Regression

The paper is devoted to developing spatial adaptive estimates for restoring functions from noisy observations. We show that the traditional least square (piecewise polynomial) estimate equipped with adaptively adjusted window possesses simultaneously many attractive adaptive properties, namely, 1) it is near– optimal within lnn–factor for estimating a function (or its derivative) at a single po...

Nonparametric estimation of a switching regression model

Estimation of a Nonparametric Censored Regression Model

In this paper we consider identiication and estimation of a censored nonparametric location scale model. We rst show that in the case where the location function is strictly less than the ((xed) censoring point for all values in the support of the explanatory variables, then the location function is not identiied anywhere. In contrast, if the location function is greater or equal to the censor-...