Nonlinear Nonparametric Regression Models
Dr. Yuedong Wang
Department of Statistics and Applied Probability
University of California, Santa Barbara
Abstract
Almost all of the current nonparametric regression methods such as
smoothing splines, generalized additive models and varying coefficients
models assume a linear relationship when nonparametric functions are
regarded as parameters. In this talk we present a general class of
nonlinear nonparametric models that allow nonparametric functions to
act nonlinearly. They arise in many fields as either theoretical or
empirical models. We propose new estimation methods based on an extension
of the Gauss-Newton method to infinite dimensional spaces and
empirical models. We propose new estimation methods based on an extension
of the Gauss-Newton method to infinite dimensional spaces and
the backfitting procedure. We extend the generalized cross validation
and the generalized maximum likelihood methods to estimate
smoothing parameters. Connections between nonlinear nonparametric
models and nonlinear mixed effects models are established. Approximate
Bayesian confidence intervals are derived for inference. We will also
present a user friendly R function for fitting these models.
The methods will be illustrated using two real data examples.