Interval linear regression analysis based on Minkowski difference - a bridge between traditional and interval linear regression models. (English) Zbl 1249.65012

Summary: In this paper we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval error. We formalize the estimation problem of parameters of the interval function so as to minimize the sum of square/absolute interval errors. Introducing suitable interpretation of minimization of an interval function, each estimation problem is well-formulated as a quadratic or linear programming problem. It is shown that the proposed methods have close relation to both traditional and interval linear regression methods which are formulated in different manners.


65C60 Computational problems in statistics (MSC2010)
65G40 General methods in interval analysis
62J05 Linear regression; mixed models
65K05 Numerical mathematical programming methods
90C05 Linear programming
90C20 Quadratic programming
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