Abstract
The similarity degree between the expectation of two random intervals is studied by means of a hypothesis testing procedure. For this purpose, a similarity measure for intervals is introduced based on the so-called Jaccard index for convex sets. The measure ranges from 0 (if both intervals are not similar at all, i.e., if they are not overlapped) to 1 (if both intervals are equal). A test statistic is proposed and its limit distribution is analyzed by considering asymptotic and bootstrap techniques. Some simulation studies are carried out to examine the behaviour of the approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aumann RJ (1965) Integrals of set-valued functions. J Math Anal Appl 12:1–12
Blanco-Fernndez A, Corral N, González-Rodríguez G (2011) Estimation of a flexible simple linear model for interval data based on set arithmetic. Comput Stat Data Anal 55(9):2568–2578
Ferraro MB, Coppi R, González-Rodríguez G, Colubi A (2010) A linear regression model for imprecise response. Int J Approximate Reasoning 51(7):759–770
González-Rodríguez G, Colubi A, Gil MA (2012) Fuzzy data treated as functional data: a one-way ANOVA test approach. Comput Stat Data Anal 56(4):943–955
Horowitz JL, Manski CF (2006) Identification and estimation of statistical functionals using incomplete data. J Econ 132:445–459
Hudgens MG (2005) On nonparametric maximum likelihood estimation with interval censoring and left truncation. J Roy Stat Soc: Ser B 67:573–587
Jaccard P (1901) tude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin de la Socit Vaudoise des Sciences Naturelles 37:547–579
Körner R (2000) An asymptotic \(\alpha \)-test for the expectation of random fuzzy variables. J Stat Plann Infer 83:331–346
Magnac T, Maurin E (2008) Partial identification in monotone binary models: discrete regressors and interval data. Rev Econ Stud 75:835–864
Matheron G (1975) Random sets and integral geometry. Wiley, New York
Molchanov I (2005) Theory of random sets. Springer, London
Ramos-Guajardo AB, Colubi A, González-Rodríguez G (2014) Inclusion degree tests for the Aumann expectation of a random interval. Inf Sci 288(20):412–422
Ramos-Guajardo AB (2015) Similarity test for the expectation of a random interval and a fixed interval. In: Grzegorzewski P, Gagolewski M, Hryniewicz O, Gil MA (eds) Strengthening links between data analysis and soft computing. Adv Intell Syst Comput 315:175–182
Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, Cambridge
Acknowledgments
The research in this paper is partially supported by the Spanish National Grant MTM2013-44212-P, and the Regional Grant FC-15-GRUPIN-14-005. Their financial support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Ramos-Guajardo, A.B., Blanco-Fernández, Á. (2017). Two-Sample Similarity Test for the Expected Value of Random Intervals. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_52
Download citation
DOI: https://doi.org/10.1007/978-3-319-42972-4_52
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42971-7
Online ISBN: 978-3-319-42972-4
eBook Packages: EngineeringEngineering (R0)