New algorithms for statistical analysis of interval data

Authors:
Gang Xiang;Scott A. Starks;Vladik Kreinovich;Luc Longpré
Affiliations:
NASA Pan-American Center for Earth and Environmental Studies (PACES), University of Texas, El Paso, TX;NASA Pan-American Center for Earth and Environmental Studies (PACES), University of Texas, El Paso, TX;NASA Pan-American Center for Earth and Environmental Studies (PACES), University of Texas, El Paso, TX;NASA Pan-American Center for Earth and Environmental Studies (PACES), University of Texas, El Paso, TX
Venue:
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Year:
2004

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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 $\widetilde x_i$. 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.