Nonparametric regression estimation in models with weak error's structure

Estimation in Nonparametric Regression with Nonregular Errors

For sufficiently nonregular distributions with bounded support, the extreme observations converge to the boundary points at a faster rate than the square root of the sample size. In a nonparametric regression model with such a nonregular error distribution, this fact can be used to construct an estimator for the regression function that converges at a faster rate than the Nadaraya– Watson estim...

Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors

More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors

We propose a modification of kernel time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that has to be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. It is shown that the proposed estimation...

Nonparametric Regression with Correlated Errors

Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivity are explained, including the breakdown of several popular data-driven smoothing parameter selection methods. We review the existing literature in kernel regression, smoothing splines and wavelet regression under correlation, both for short-range an...

Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem

In the classical errors-in-variables problem, the goal is to estimate a regression curve from data in which the explanatory variable is measured with error. In this context, nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed. Although there are many situations in which this assumption is too restrictive, nonparametric est...