article

A resampling approach for interval-valued data regression

Authors:

Yongho JeonAuthors Info & Claims

Statistical Analysis and Data Mining, Volume 5, Issue 4

Pages 336 - 348

https://doi.org/10.1002/sam.11150

Published: 01 August 2012 Publication History

Abstract

We consider interval-valued data that frequently appear with advanced technologies in current data collection processes. Interval-valued data refer to the data that are observed as ranges instead of single values. In the last decade, several approaches to the regression analysis of interval-valued data have been introduced, but little work has been done on relevant statistical inferences concerning the regression model. In this paper, we propose a new approach to fit a linear regression model to interval-valued data using a resampling idea. A key advantage is that it enables one to make inferences on the model such as the overall model significance test and individual coefficient test. We demonstrate the proposed approach using simulated and real data examples, and also compare its performance with those of existing methods. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012 © 2012 Wiley Periodicals, Inc.

References

[1]

E. Diday, An introduction to symbolic data analysis and the sodas software, J Symbolic Data Anal 7 (2003), 1723–5081.

[2]

L. Billard and E. Diday, From the statistics of data to the statistics of knowledge: Symbolic data analysis, J Am Stat Assoc 98 (2003), 470–487.

[3]

L. Billard and E. Diday, Symbolic Data Analysis: Conceptual Statistics and Data Mining, Chichester, Wiley, 2007.

[4]

E. Diday, Probabilist, possibilist and belief object for knowledge analysis, Ann Oper Res 55 (1995), 227–276.

[5]

E. Diday and R. Emilion, Lattices and capacities in analysis of probabilist object, In Studies in Classification, E. Diday, Y. Lechevallier, and O. Opilz, eds. 1996, 13–30.

[6]

E. Diday and R. Emilion, Capacities and credibilities in analysis of probabilistic objects by histograms and lattices, In Data Science, Classification, and Related Methods, C. Hayashi, N. Ohsumi, K. Yajima, Y. Tanaka, H. H. Bock, and Y. Baba, eds. 1998, 353–357.

[7]

L. Billard, Brief overview of symbolic data and analytic issues, Stat Anal Data Mining 4 (2011), 149–156.

Digital Library

[8]

M. Noirhomme-Fraiture and P. Brito, Far beyond the classical data models: symbolic data analysis, Stat Anal Data Mining 4 (2011), 157–170.

Digital Library

[9]

L. Billard and E. Diday, Regression analysis for interval-valued data, In Data Analysis, Classification, and Related Methods, H. A. L. Kiers, J.-P. Rassoon, P. J. F. Groenen, and M. Schader, eds. Berlin, Springer-Verlag, 2000, 369–374.

[10]

L. Billard and E. Diday, Symbolic regression analysis, In Classification, Clustering and Data Analysis: Proceedings of the 8th Conference of the International Federation of Classification Societies (IFCS '02), Springer, Poland,2002, 281–288.

[11]

E. A. Lima Neto, F. A. T. de Carvalho, and C. P. Tenorio, Univariate and multivariate linear regression methods to predict interval-valued features, Lecture Notes in Computer Science, AI 2004 Advances in Artificial Intelligence, Berlin, Springer-Verlag, 2004, 526–537.

Digital Library

[12]

E. Lima Neto, and F. de Carvalho, Constrained linear regression models for symbolic interval-valued variables, Comput Stat Data Anal 54 (2010), 333–347.

Digital Library

[13]

W. Xu, Symbolic Data Analysis: Interval-Valued Data Regression, Ph.D. Thesis; University of Georgia, 2010.

[14]

L. Billard, Dependencies and variation components of symbolic interval-valued data, In Selected Contributions in Data Analysis and Classification, P. Brito, G. Cucumel, P. Bertrand, and F. de Carvalho, eds. Berlin, Springer-Verlag, 2007, 3–13.

[15]

L. Billard, Sample covariance functions for complex quantitative data, In World Congress, International Association of Computational Statistics, Yokohama, Japan, 2008.

[16]

F. Alfonso, L. Billard, and E. Diday, Symbolic linear regression with taxonomies, In Classification, Clustering and Data Mining Applications, D. Banks, L. House, F. McMorris, P. Arabie, and W. Gaul, eds. Berlin, Springer-Verlag, 2004, 429–437.

[17]

A. Maia and F. D. Carvalho, Fitting a least absolute deviation regression model on symbolic interval data, Lecture Notes in Artificial Intelligence: Proceedings of the Ninth Brazilian Symposium on Artificial Intelligence, Berlin, Springer-Verlag, 2008, 207–216.

[18]

E. A. Lima Neto, G. M. Cordeiro, F. A. T. Carvalho, U. Anjos, and A. Costa, Bivariate generalized linear model for interval-valued variables, In Proceedings 2009 IEEE International Joint Conference on Neural Networks, Vol. 1, Atlanta, USA, 2009, 2226–2229.

[19]

E. Lima Neto, G. Cordeiro and F. de Carvalho, Bivariate symbolic regression models for interval-valued variables, J Stat Comput Simul 81 (2011), 1727–1744.

[20]

A. Silva, E. A. Lima Neto, and U. Anjos, A regression model to interval-valued variables based on copula approach, In Proceedings of the 58th World Statistics Congress of the International Statistical Institute, Dublin, Ireland, 2011.

[21]

E. Lima Neto, and F. de Carvalho, Center and range method for fitting a linear regression model to symbolic interval data, Comput Stat Data Anal 52 (2008), 1500–1515.

Digital Library

[22]

P. Bertrand and F. Goupil, Descriptive statistics for symbolic data, In Analysis of Symbolic Data, H.-H. Bock and E. Diday, eds. Berlin, Springer-Verlag, 2000, 103–124.

[23]

P. Good, Resampling Methods, Birkhauser, 2006.

Cited By

Dawn SBandyopadhyay S(2023)IV-GNN : interval valued data handling using graph neural networkApplied Intelligence10.1007/s10489-022-03780-153:5(5697-5713)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1007/s10489-022-03780-1
Borisov MMarkov S(2022)On the Numerical Simulation of Exponential Decay and Outbreak Data Sets Involving UncertaintiesNumerical Methods and Applications10.1007/978-3-031-32412-3_8(85-99)Online publication date: 22-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-32412-3_8
Giordani P(2018)Lasso-constrained regression analysis for interval-valued dataAdvances in Data Analysis and Classification10.1007/s11634-014-0164-89:1(5-19)Online publication date: 14-Dec-2018
https://dl.acm.org/doi/10.1007/s11634-014-0164-8
Show More Cited By

Recommendations

Linear regression with interval-valued data

Interval-valued data refers to collection of observations in the form of intervals, rather than single numbers. It originally arose from situations of imprecision due to factors such as measurement or computation errors, where intervals are used to ...
Linear regression with interval-valued data

Interval-valued data refers to collection of observations in the form of intervals, rather than single numbers. It originally arose from situations of imprecision due to factors such as measurement or computation errors, where intervals are used to ...
Linear regression with interval-valued data

Interval-valued data refers to collection of observations in the form of intervals, rather than single numbers. It originally arose from situations of imprecision due to factors such as measurement or computation errors, where intervals are used to ...

Comments

Information & Contributors

Information

Published In

cover image Statistical Analysis and Data Mining

Statistical Analysis and Data Mining Volume 5, Issue 4

August 2012

88 pages

ISSN:1932-1864

EISSN:1932-1872

Issue’s Table of Contents

Publisher

John Wiley & Sons, Inc.

United States

Publication History

Published: 01 August 2012

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 09 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Dawn SBandyopadhyay S(2023)IV-GNN : interval valued data handling using graph neural networkApplied Intelligence10.1007/s10489-022-03780-153:5(5697-5713)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1007/s10489-022-03780-1
Borisov MMarkov S(2022)On the Numerical Simulation of Exponential Decay and Outbreak Data Sets Involving UncertaintiesNumerical Methods and Applications10.1007/978-3-031-32412-3_8(85-99)Online publication date: 22-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-32412-3_8
Giordani P(2018)Lasso-constrained regression analysis for interval-valued dataAdvances in Data Analysis and Classification10.1007/s11634-014-0164-89:1(5-19)Online publication date: 14-Dec-2018
https://dl.acm.org/doi/10.1007/s11634-014-0164-8
Hao PGuo J(2017)Constrained center and range joint model for interval-valued symbolic data regressionComputational Statistics & Data Analysis10.1016/j.csda.2017.06.005116:C(106-138)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1016/j.csda.2017.06.005

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents