Nonlinear Regression with Structured Inputs

• Activity Number: 176
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Sandy Balkin*+
• Affiliation(s): Pfizer, Inc.
• Keywords: Model Selection ; Orthogonality ; Prediction

Abstract

For many applications of nonlinear regression, theory does not guide the model-building process by suggesting a relevant functional form. This research develops a new technique for use in this situation. Called STAT-ANN, the method provides modeling flexibility similar to a neural network, but provides a statistical basis for model selection, interpretation, and validation by following a two-step process. We first generate an extended input basis and then fit a nonlinear prediction function. We present a theoretical derivation of the new method, prove that it is a universal function approximator, and develop a model-building paradigm. The new approach also allows the investigator to gain some insights into the data generating process, while eliminating the need choose a specific nonlinear regression function. Finally, we demonstrate the use of the method on various business applications.