Integrated Gaussian Process and Monotone Smoothing without Splines

• Activity Number: 526
• Type: Contributed
• Date/Time: Thursday, August 11, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Farideh Dehkordi-Vakil*+
• Companies: Western Illinois University
• Keywords: Monotone Smoothing ; Regression ; Integrated Gaussian Process

Abstract

Recent contributions to the subject of monotone smoothing are generally based on piecewise polynomials and splines, using either optimization or Bayesian techniques to estimate the parameters. Although these methods generally produce satisfactory results, they tend to overparametrize the parameter space and over smooth (note that except perhaps at knots, piecewise polynomials have derivatives of all orders). Methods that use optimization techniques to estimate the model parameters also need to deal with the problem of selecting the number and location of the knots, and of writing codes that suit their specific problems. In this paper, we propose a method that avoids these problems. Our model uses an integral representation of smooth monotone functions that is similar to the one J. Ramsay has used. Our Bayesian approach to estimate the parameters leads to a stochastic integral equation, which we turn into a model involving an integrated Gaussian process using a linearization technique. The implementation of our method also requires a suitable transformation.