B. Seifert Th. Gasser University of Zurich Department of Biostatistics Sumatrastrasse 30 CH{8006 Z urich, Switzerland Abstract When estimating a regression function r or its th derivative, local polynomials are an attractive choice due to their exibility and asymptotic performance. Seifert & Gasser (1996) proposed local polynomial ridging to overcome problems of local polynomials with variance...

Many practical problems require nonparametric estimates of regression functions, and local polynomial regression has emerged as a leading approach. In applied settings practitioners often adopt either the local constant or local linear variants, or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative estimate required. But such ad hoc determin...

Locally weighted polynomial regression (LWPR) is a popular instance-based algorithm for learning continuous non-linear mappings. For more than two or three inputs and for more than a few thousand datapoints the computational expense of predictions is daunting. We discuss drawbacks with previous approaches to dealing with this problem, and present a new algorithm based on a multiresolution searc...

Jin Wang MSc Student, School of Material Science and Engineering, University of Science and Technology Beijing, Beijing, China Aizhi Sun Associate Professor, School of Material Science and Engineering, University of Science and Technology Beijing, Beijing, China Qian Gao PhD Professor, School of Civil and Environment Engineering, University of Science and Technology Beijing, Beijing, China Fuqi...

We propose a new approach to conditional quantile function estimation that combines both parametric and nonparametric techniques. At each design point, a global, possibly incorrect, pilot parametric model is locally adjusted through a kernel smoothing fit. The resulting quantile regression estimator behaves like a parametric estimator when the latter is correct and converges to the nonparametri...

This paper derives the exact functional form of an error contaminated regression function when the error free regression is a polynomial function of error free covariates (discrete or continuous) which are contaminated by normally distributed measurement error, with coe¢cients which may be arbitrary functions of error free covariates. The form of higher order central moment error contaminated r...

Asymptotically exact and conservative confidence bands are obtained for a nonparametric regression function, using piecewise constant and piecewise linear spline estimation, respectively. Compared to the pointwise confidence interval of Huang (2003), the confidence bands are inflated by a factor proportional to {log (n)}, with the same width order as the Nadaraya-Watson bands of Härdle (1989), ...

The selection of an optimal regression model comprising linear combinations of various integer powers of an independent variable (explanatory variables) is considered. The optimal model is defined as the most accurate (minimal variance) stable model, where all parameter estimates of the orthogonalized explanatory variables are significantly different from zero. The potential causes that limit t...

The approach of subset selection in polynomial regression model building assumes that the chosen fixed full set of predefined basis functions contains a subset that is sufficient to describe the target relation sufficiently well. However, in most cases the necessary set of basis functions is not known and needs to be guessed – a potentially non-trivial (and long) trial and error process. In our...

This paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data, with the key idea of using generalised inverses of correlation matrices. The estimator has a simple closed-form expression. Simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation. Our approach can be char...