Experimental Designs for Fitting Segmented Polynomial Regression Models

Abstract

In many applications a response variable, y, may not be adequately represented by a polynomial function of the input variable, x, over the entire experimental space. Often a desirable choice of a regression model is one which consists of grafted polynomial submodels.

This paper mainly considers the problem of finding minimum point experimental designs to estimate the coefficients in segmented polynomial regression. For the efficiency of estimation. the D-optimality design criterion (which minimizes the generalized variance of the least squares estimates of the unknown parameters) is adopted.

KEY WORDS:

• Segmented polynomial regression
• Spline function
• D-optimal designs
• Response surfaces
• Nonlinear estimation