Recursive local polynomial regression under dependence conditions

Local polynomial estimation in partial linear regression models under dependence

A regression model whose regression function is the sum of a linear and a nonparametric component is presented. The design is random and the response and explanatory variables satisfy mixing conditions. A new local polynomial type estimator for the nonparametric component of the model is proposed and its asymptotic normality is obtained. Specifically, this estimator works on a prewhitening tran...

On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data

Motivated by the analysis of glomerular time series extracted from calciumimaging data, asymptotic theory for piecewise polynomial and spline regression with partially free knots and residuals exhibiting three types of dependence structures (long memory, short memory and anti-persistence) is considered. Unified formulas based on fractional calculus are derived for subordinated residual processe...

Asymptotics for polynomial spline regression under weak conditions

We derive rate of convergence for spline regression under weak conditions. The results improve upon those in Huang (Ann. Statist. 26 (1998a) 242) in two ways. Firstly, results are obtained under less stringent conditions on the growing rate of the number of knots. Secondly, L2 approximation instead of L∞ approximation by splines are used to bound the rate of convergence, this allows us to obtai...

Local Polynomial Regression

Local Polynomial Regression and SIMEX

This paper introduces a new local polynomial estimator and develops supporting asymptotic theory for non-parametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski’s simulation-extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by (1) using a bandwidth selection procedu...