Empirical likelihood estimators for the error distribution in nonparametric regression models

Empirical likelihood estimators for the error distribution in nonparametric regression models

Testing for Symmetric Error Distribution in Nonparametric Regression Models

For the problem of testing symmetry of the error distribution in a nonparametric regression model, we investigate the asymptotic properties of the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covariance structure of this process dep...

Penalized Likelihood-type Estimators for Generalized Nonparametric Regression

We consider the asymptotic analysis of penalized likelihood type estimators for generalized non-parametric regression problems in which the target parameter is a vector valued function defined in terms of the conditional distribution of a response given a set of covariates. A variety of examples including ones related to generalized linear models and robust smoothing are covered by the theory. ...

Empirical Likelihood for Nonparametric Additive Models

Nonparametric additive modeling is a fundamental tool for statistical data analysis which allows flexible functional forms for conditional mean or quantile functions but avoids the curse of dimensionality for fully nonparametric methods induced by high-dimensional covariates. This paper proposes empirical likelihood-based inference methods for unknown functions in three types of nonparametric a...

Asymptotically optimal differenced estimators of error variance in nonparametric regression

The existing differenced estimators of error variance in nonparametric regression are interpreted as kernel estimators, and some requirements for a ‘‘good’’ estimator of error variance are specified. A new differenced method is then proposed that estimates the errors as the intercepts in a sequence of simple linear regressions and constructs a variance estimator based on estimated errors. The n...