New Algorithms for Statistical Analysis of Interval Data

Authors

Gang Xiang
Scott A. Starks, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow

Publication Date

5-2005

Comments

UTEP-CS-04-04b.

Short version published in Proceedings of the Workshop on State-of-the-Art in Scientific Computing PARA'04, Lyngby, Denmark, June 20-23, 2004, Vol. 1, pp. 123-129; extended version published in Jack Dongarra, Kaj Madsen, and Jerzy Wasniewski (eds.), PARA'04 Workshop on State-of-the-Art in Scientific Computing, Springer Lecture Notes in Computer Science, 2006, Vol. 3732, pp. 189-196.

Abstract

It is known that in general, statistical analysis of interval data is an NP-hard problem: even computing the variance of interval data is, in general, NP-hard. Until now, only one case was known for which a feasible algorithm can compute the variance of interval data: the case when all the measurements are accurate enough -- so that even after the measurement, we can distinguish between different measured values Xi. In this paper, we describe several new cases in which feasible algorithms are possible -- e.g., the case when all the measurements are done by using the same (not necessarily very accurate) measurement instrument -- or at least a limited number of different measuring instruments.