Nonparametric Regression Estimation with Mixed Measurement Errors

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...

Measurement Errors Regression: a Nonparametric Approach

Nonparametric regression provides a useful tool for exploring the association between the responses and covariates. In many applications, the actual values of the covariates are not known, but are measured with errors or through surrogates. In this paper, we present nonparametric regression techniques to study the association between the response and the underlying unobserved covariate. Deconvo...

Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors

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...

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...