Statistics and Data Science Seminar
Prof. Lijian Yang
MIchigan State University
Spline Single-Index Prediction Model
Abstract: For the past two decades, single-index model, a special case of projection
pursuit regression, has proven to be an efficient way of coping with the high
dimensional problem in nonparametric regression. Applications of single-index
model lie in a variety of fields, such as discrete choice analysis in
econometrics and dose-response models in biometrics, where high-dimensional
regression models are often employed. We investigate the single-index prediction
based on weakly dependent sample. The single-index is identified by the best
approximation to the multivariate prediction function of the response variable,
regardless of whether the prediction function is a genuine single-index
function. A polynomial spline estimator is proposed for the single-index
coefficients, and is shown to be strongly consistent and asymptotically normal.
An iterative program based on Newton-Raphson algorithm is developed. The
algorithm is sufficiently fast for the user to analyze large data of high
dimension within seconds. Simulation experiments have provided strong evidence
that corroborates with the asymptotic theory. Finally, we illustrate our
estimation procedure by a gas furnace example.
Wednesday March 7, 2007 at 3:30 PM in SEO 712