Efficient evaluation of the sample variance of an interval-valued dataset

3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015

数学;化学;物理学

erný, Michal^1

Department of Econometrics, University of Economics Prague, Winston Churchill Square 4, Prague

13067, Czech Republic^1

关键词: Exponential time;    Interval-valued;    Interval-valued data;    Np-hardness results;    Probabilistic modeling;    Probabilistic process;    Simulation studies;    Variation coefficient;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/622/1/012031/pdf
DOI  :  10.1088/1742-6596/622/1/012031

来源: IOP

【 摘 要 】

Given a set of interval-valued data, a general problem is to compute bounds for a particular statistic, such as sample mean or variance, variation coefficient or entropy. It is well known that computation of the upper bound of sample variance is an NP-hard problem. Here we consider a variant of an algorithm by Fersonet al., which is exponential in the worst case, and investigate its behavior under a natural probabilistic model. A simulation study shows that the undesirable case, which forces the algorithm to work in exponential time (and which appears in the proof of NP-hardness), occurs very rarely in an environment when the interval data are generated by probabilistic processes which are natural from a statistical viewpoint. The main finding is that the thealgorithm is practically very efficient and that the NP-hardness result usually "does not matter too much".