Adaptive estimation under single-index constraint in a regression model

Estimation of single-index quantile regression Model

Abstract The conditional quantile function m(X) of response variable Y given the value of covariate X is modeled through a single-index model, i.e. m(X) = m(θ 0 X) for some unknown parameter vector θ0. An iterated algorithm is proposed to estimate θ0. To establish the root-n consistency of the estimator, we prove a convexity lemma for almost sure convergence, parallel to the results by Pollard ...

Conditional density estimation in a censored single-index regression model

A Single-index Quantile Regression Model and Its Estimation

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...

Laguerre Estimation under Constraint at a Single Point

This paper presents a general methodology for nonparametric estimation of a function s related to a nonnegative real random variable X, under a constraint of type s(0) = c. Three different examples are investigated: the direct observations model (X is observed), the multiplicative noise model (Y = XU is observed, with U following a uniform distribution) and the additive noise model (Y = X + V i...