Asymmetric least squares regression estimation: A nonparametric approach∗

Nonparametric regression estimation using penalized least squares

We present multivariate penalized least squares regression estimates. We use Vapnik{ Chervonenkis theory and bounds on the covering numbers to analyze convergence of the estimates. We show strong consistency of the truncated versions of the estimates without any conditions on the underlying distribution.

Nonparametric Least Squares Estimation in Derivative Families

Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose series-type estimators which incorporate various derivative data into a single, weighted, nonparametric, least-squares procedure. Convergence rates are obtained, w...

Asymmetric Least Squares Estimation and Testing

A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression

Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares es...

Local nonlinear least squares: Using parametric information in nonparametric regression

We introduce a new nonparametric regression estimator that uses prior information on regression shape in the form of a parametric model. In e!ect, we nonparametrically encompass the parametric model. We obtain estimates of the regression function and its derivatives along with local parameter estimates that can be interpreted from within the parametric model. We establish the uniform consistenc...