The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing

Abstract

This article shows how to fit a smooth curve (polynomial spline) to pairs of data values (y_i, x_i ). Prior specification of a parametric functional form for the curve is not required. The resulting curve can be used to describe the pattern of the data, and to predict unknown values of y given x. Both point and interval estimates are produced. The method is easy to use, and the computational requirements are modest, even for large sample sizes. Our method is based on maximum likelihood estimation of a signal-in-noise model of the data. We use the Kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem.

Key Words:

• Nonparametric regression
• Splines
• Kalman filter