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

Inuiguchi, Masahiro; Tanino, Tetsuzo

Kybernetika 42, No. 4, 423-440 (2006).

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.

MSC:

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

Keywords:

interval linear regression analysis; least squares method; minimum absolute deviations method; Minkowski difference; numerical input; interval output; interval equation; interval function; quadratic or linear programming problem

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