Optimal Designs for Rational Function Regression

• Activity Number: 511
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): David Papp*+
• Companies: Rutgers University
• Keywords: Optimal design ; Rational function regression ; Semidefinite programming ; Nonlinear regression

Abstract

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method generates a polynomial whose zeros are the support points of the optimal approximate design, and generalizes a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved very efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of both its convergence and its algorithmic efficacy. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found.