Newton Method for Interval Predictor Model with Sphere Parameter Set

Abstract

In this paper, we study the construction of interval prediction model. After introducing the family of models and some basic information, we present the computational results for the construction of interval predictor models, using linear regression structures which regression parameters are included in a sphere parameter set. Given a size measure to scale the average amplitude of the predictor interval, one optimal model that minimizes a size measure is efficiently computed by solving a linear programming problem, firstly we apply the active set approach to solve the linear programming problem and propose one Newton iterative form of the optimization variables. Based on these optimization variables, the predictor interval of the considered model with sphere parameter set can be directly constructed. Secondly as for a fixed non-negative number from the size measure, we propose a better choice by using the Karush-Kuhn-Tucker optimality conditions.