Organizer:

Andreas Buja, andreas@research.att.com

Speakers

10:15 a.m.
A Computationally Efficient Oracle Estimator for Additive Nonparametric Regression with Bootstrap Confidence Intervals
Oliver B. Linton, Yale University
(joint work with W. Kim and N.W. Hengartner, Yale University)

This paper makes three contributions. First, we introduce a computationally efficient estimator for the component functions in additive nonparametric regression exploiting a different motivation from the marginal integration estimator of Linton and Nielsen (1995). Our method provides a reduction in computation of order n, which is highly significant in practice. Second, we define an efficient estimator of the additive components, by inserting the preliminary estimator into a backfitting algorithm but taking one step only, and establish that it is equivalent in various sense to the oracle estimator based on knowing the other components. Our two-step estimator is minimax superior to that considered in Opsomer and Ruppert (1997), due to its better bias. Third, we define a bootstrap algorithm for computing pointwise confidence intervals and show that it achieves the correct coverage.

11:10 a.m.
A Root-n Consistent Backfitting Estimator for Semiparametric Additive Modelling
Jean Opsomer, Iowa State University
(joint work with David Ruppert, Cornell University)

We explore additive models that combine both parametric and nonparametric terms and propose a root-n consistent backfitting estimator for the parametric component of the model. The theoretical properties of the estimator are developed for the case with a single nonparametric term and extended to an arbitrary number of nonparametric additive terms. An estimator for the optimal bandwidth making minimal use of asymptotic expressions for bias and variance is proposed, and a fast implementation algorithm for model fitting and bandwidth selection is developed. The practical behavior of the estimator and bandwidth selection is illustrated by simulation experiments.