[Home ] [Archive]    
Main Menu
Journal Information::
Home::
Archive::
For Authors::
For Reviewers::
Principles of Transparency::
Contact us::
::
Search in website

Advanced Search
..
Committed to

AWT IMAGE

Attribution-NonCommercial
CC BY-NC


AWT IMAGE

Open Access Publishing


AWT IMAGE

Prevent Plagiarism

..
Registered in


..
Statistics
Journal volumes: 17
Journal issues: 34
Articles views: 683905
Articles downloads: 342215

Total authors: 581
Unique authors: 422
Repeated authors: 159
Repeated authors percent: 27

Submitted articles: 368
Accepted articles: 266
Rejected articles: 25
Published articles: 219

Acceptance rate: 72.28
Rejection rate: 6.79

Average Time to Accept: 282 days
Average Time to First Review: 27.2 days
Average Time to Publish: 26.1 days

Last 3 years statistics:
Submitted articles: 54
Accepted articles: 37
Rejected articles: 6
Published articles: 17

Acceptance rate: 68.52
Rejection rate: 11.11

Average Time to Accept: 205 days
Average Time to First Review: 6.7 days
Average Time to Publish: 118 days
____
..
:: Volume 15, Issue 2 (3-2019) ::
JSRI 2019, 15(2): 237-274 Back to browse issues page
Assessment and Estimation of the Coefficients of a Linear Model for Interval Data
Amir Massoud Malekfar 1, Farzad Eskandari2
1- Allameh Tabataba'i University , malekfar1364@gmail.com
2- Allameh Tabataba'i University
Abstract:   (1687 Views)
Imprecise measurement tools produce imprecise data. Interval,-valued (interval) data is ‌one type of data ‌which is usually ‌used to deal with such imprecision. So,‌ interval-valued variables have been used in the last decade. The relationships between the variables have recently ‌been modeled by linear regression models. If interval response variables have any statistical distributions, the relationships are ‌modeled in the linear models framework. In this paper, we propose new estimators for the parameters of an interval linear model under some conditions. Under the conditions, we demonstrate the theoretical adequacy of the estimators. Simulation studies and a real-life case study show the empirical adequacy and the practical applicability of the new estimators, respectively, under the conditions.
Keywords: Interval-valued data, interval linear model, ‌the theoretical and empirical adequacy of the estimators
Full-Text [PDF 1946 kb]   (1066 Downloads)    
Type of Study: Research | Subject: General
Received: 2018/01/14 | Accepted: 2019/11/5 | Published: 2019/12/8
References
1. Afonso, F., Billard, L., Diday, E. and Limam, M. (2007). Symbolic Linear Regression Methodology. Symbolic Data Analysis and the SODAS Software, 359-372. [DOI:10.1002/9780470723562.ch19]
2. Artstein, Z. and Vitale, R.A. (1975). A Strong Law of Large Numbers for Random Compact Sets. Ann. Probability, 5, 879-882. [DOI:10.1214/aop/1176996275]
3. Bertrand, P. and Goupil, F. (2000). Descriptive Statistics for Symbolic Data. In Bock, H.H. and Diday, E. (eds) Analysis of Symbolic Data (pp. 106-124). Studies in Classification, Data Analysis, and Knowledge Organization. Springer Berlin Heidelberg. [DOI:10.1007/978-3-642-57155-8_6]
4. Billard, L. (2007). Dependencies and Variation Components of Symbolic Interval-valued Data. In Brito, P., Cucumel, G., Bertrand, P. and de Carvalho, F. (eds) Selected Contributions in Data Analysis and Classification (pp. 3-12). Studies in Classification, Data Analysis, and Knowledge Organization. Springer Berlin Heidelberg. [DOI:10.1007/978-3-540-73560-1_1]
5. Billard, L. (2011). Brief Overview of Symbolic Data and Analytic Issues. Stat. Anal. Data Min., 4, 149-156. [DOI:10.1002/sam.10115]
6. Billard, L. and Diday, E. (2000). Regression Analysis for Interval-valued Data. In Kiers, H.A.L., Rasson, J.P., Groenen, P.J.F. and Schader, M. (eds) Data Analysis, Classification, and Related Methods (pp. 369-374). Studies in Classification, Data Analysis, and Knowledge Organization. Springer Berlin Heidelberg. [DOI:10.1007/978-3-642-59789-3_58]
7. Blanco-Fernandez, A., Corral, N. and Gonzalez-Rodriguez, G. (2011). Estimation of a Flexible Simple Linear Model for Interval Data Based on Set Arithmetic. Comput. Statist. Data Anal., 55, 2568-2578. [DOI:10.1016/j.csda.2011.03.005]
8. Calle, M.L. and Gomez, G. (2001). Nonparametric Bayesian Estimation from Interval-censored Data Using Monte Carlo Methods. J. Statist. Plann. Inference, 98, 73-87. [DOI:10.1016/S0378-3758(00)00320-7]
9. Diday, E. (1995). Probabilist, Possibilist and Belief Objects for Knowledge Analysis. Annal. Operat. Research, 55, 225-276. [DOI:10.1007/BF02030862]
10. Diday, E. and Emilion, R. (1998). Capacities, Credibilities in Analysis of Probabilistic Objects by Histograms and Lattices. In Hayashi, C., Yajima, K., Bock, H.H., Ohsumi, N., Tanaka, Y. and Baba, Y. (eds) Data Science, Classification, and Related Methods (pp. 353-357). Studies in Classification, Data Analysis, and Knowledge Organization. Springer Tokyo. [DOI:10.1007/978-4-431-65950-1_39]
11. Emilion, R. (1997). Differentiation des Capacites et des Integrales de Choquet. Comptes Rendus de l'Académie des Sciences. Mathématique, 324, 389-392. [DOI:10.1016/S0764-4442(97)80073-0]
12. Gil, M.A., Gonzalez-Rodriguez, G., Colubi, A. and Montenegro, M. (2007). Testing Linear Independence in Linear Models with Interval-valued Data. Comput. Statist. Data Anal., 51, 3002-3015. [DOI:10.1016/j.csda.2006.01.015]
13. Huber, C., Solev, V. and Vonta, F. (2009). Interval Censored and Truncated Data: Rate of Convergence of NPMLE of the Density. J. Statist. Plann. Inference, 139, 1734-1749. [DOI:10.1016/j.jspi.2008.05.028]
14. Kim, J. and Billard, L. (2011). A Polythetic Clustering Process and Cluster Validity Indexes for Histogram-valued Objects. Comput. Statist. Data Anal., 55, 2250-2262. [DOI:10.1016/j.csda.2011.01.011]
15. Le-Rademacher, J. and Billard, L. (2012). Symbolic Covariance Principal Component Analysis and Visualization for Interval-valued Data. J. Comput. Graph. Statist., 21, 413-432. [DOI:10.1080/10618600.2012.679895]
16. Neto, E.A.L. and de Carvalho, F.A.T. (2008). Centre and Range Method for Fitting a Linear Regression Model to Symbolic Interval Data. Comput. Statist. Data Anal., 52, 1500-1515. [DOI:10.1016/j.csda.2007.04.014]
17. Neto, E.A.L. and de Carvalho, F.A.T. (2010). Constrained Linear Regression Models for Symbolic Interval-valued Variables. Comput. Statist. Data Anal., 54, 333-347. [DOI:10.1016/j.csda.2009.08.010]
18. Neto, E.A.L., de Carvalho, F.A.T. and Tenorio, C. P. (2004). Univariate and Multivariate Linear Regression Methods to Predict Interval-valued Features. In The Australasian Joint Conference on Artificial Intelligence (pp. 526-537). Springer Berlin Heidelberg. [DOI:10.1007/978-3-540-30549-1_46]
19. Neto, E.A.L., de Carvalho, F.A.T. and Freire, E.S. (2005). Applying Constrained Linear Regression Models to Predict Interval-valued Data. In The Annual Conference on Artificial Intelligence (pp. 92-106). Springer Brelin Heidelberg. [DOI:10.1007/11551263_9]
20. Rivero, C. and Valdes, T. (2008). An Algorithm for Robust Linear Estimation with Grouped Data. Comput. Statist. Data Anal., 53, 255-271. [DOI:10.1016/j.csda.2008.07.009]
21. Trutschnig, W., Gonzalez-Rodriguez, G., Colubi, A. and Gil, M.A. (2009). A New Family of Metrics for Compact, Convex (Fuzzy) Sets Based on a Generalized Concept of Mid and Spread. Inform. Sci., 179, 3964-3972. [DOI:10.1016/j.ins.2009.06.023]
22. Wang, H., Guan, R. and Wu, J. (2012). Linear Regression of Interval-valued Data Based on Complete Information in Hypercubes. J. Syst. Sci. Syst. Eng., 21, 422-442. [DOI:10.1007/s11518-012-5203-4]
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA



XML   Persian Abstract   Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Malekfar A M, Eskandari F. Assessment and Estimation of the Coefficients of a Linear Model for Interval Data. JSRI 2019; 15 (2) :237-274
URL: http://jsri.srtc.ac.ir/article-1-310-en.html


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 15, Issue 2 (3-2019) Back to browse issues page
مجله‌ی پژوهش‌های آماری ایران Journal of Statistical Research of Iran JSRI
Persian site map - English site map - Created in 0.05 seconds with 41 queries by YEKTAWEB 4645