Foundations of Statistical Processing of Set-Valued Data: Towards Efficient Algorithms

Authors

Hung T. Nguyen
Vladik Kreinovich, The University of Texas at El PasoFollow
Gang Xiang

Publication Date

11-2004

Comments

UTEP-CS-04-35.

Published in Proceedings of the Fifth International Conference on Intelligent Technologies InTech'04, Houston, Texas, December 2-4, 2004.

Abstract

Due to measurement uncertainty, often, instead of the actual values xi of the measured quantities, we only know the intervals [Xi]=[Xi-Di,Xi+Di], where Xi is the measured value and Di is the upper bound on the measurement error (provided, e.g., by the manufacturer of the measuring instrument). These intervals can be viewed as random intervals, i.e., as samples from the interval-valued random variable. In such situations, instead of the exact value of a sample statistic such as covariance C(x,y), we can only have an interval [C](x,y) of possible values of this statistic.

In this paper, we extend the foundations of traditional statistics to statistics of such set-valued data, and describe how this foundation can lead to efficient algorithms for computing the corresponding set-valued statistics.