Testing linear independence in linear models with interval-valued data

Computational Statistics and Data Analysis

Volumn 51, Issue 6, 2007, Pages 3002-3015

  Gil, María Ángeles ^a   González Rodríguez, Gil ^a   Colubi, Ana ^a   Montenegro, Manuel ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Bootstrap; Interval arithmetic based approach; Interval valued random set; Large sample theory; Mid spread representation; Simple linear model for random intervals

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; REGRESSION ANALYSIS; SET THEORY;

BOOTSTRAP TECHNIQUES; INTERVAL ARITHMETIC-BASED APPROACH; INTERVAL VALUED RANDOM SET; LARGE SAMPLE THEORY; MID SPREAD REPRESENTATION; SIMPLE LINEAR MODEL FOR RANDOM INTERVALS;

STATISTICAL TESTS;

EID: 33846807389     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.01.015     Document Type: Article

References (29)

1. Adler J. Bootstrap percolation. Physica A 171 (1991) 453-470
2. Artstein Z., and Vitale R.A. A strong law of large numbers for random compact sets. Ann. Probab. 3 (1975) 879-882
3. Aumann R.J. Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965) 1-12
4. Beran R., and Srivastava M.S. Bootstrap tests and confidence regions for functions of a covariance matrix. Ann. Statist. 13 (1985) 95-115
5. Billard L., and Diday E. From the statistics of data to the statistics of knowledge: symbolic data analysis. J. Amer. Statist. Assoc. 98 (2003) 470-487
6. Billingsley P. Probability and Measure. third ed (1995), Wiley, New York
7. Cressie N.A.C. Statistics for Spatial Data (1993), Wiley, New York
8. De Carvalho F.A.T., Lima Neto E.A., and Tenorio C.P. A new method to fit a linear regression model for interval-valued data. In: Biundo S., Frühwirth T., and Palm G. (Eds). Proceedings of the 27th German Conference on Artificial Intelligence, KI 2004, Ulm, Germany, Lectures Notes on Artificial Intelligence vol. 3238 (2004), Springer, Heidelberg 295-306
9. Diamond P. Least squares fitting of compact set-valued data. J. Math. Anal. Appl. 14 (1990) 531-544
10. Efron B. Censored data and the bootstrap. J. Amer. Statist. Assoc. 76 (1981) 312-319
11. García-Soidán P.H., and Hall P. On sample reuse methods for spatial data. Biometrics 53 (1997) 273-281
12. Gil, M.A., López-García, M.T., Lubiano, M.A., Montenegro, M., 2000. A linear correlation coefficient for interval-valued random sets. Proceedings of the Eighth International Conference IPMU, vol. 1, pp. 104-110.
13. Gil M.A., López-García M.T., Lubiano M.A., and Montenegro M. Regression and correlation analyses of a linear relation between random intervals. Test 10 (2001) 183-201
14. Gil M.A., Lubiano M.A., Montenegro M., and López-García M.T. Least squares fitting of an affine function and strength of association for interval-valued data. Metrika 56 (2002) 97-111
15. Hall P., Melville G., and Welsh A.H. Bias correction and bootstrap methods for a spatial sampling scheme. Bernoulli 7 (2001) 829-846
16. Hess C. Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. Ann. Statist. 24 (1996) 1298-1315
17. James L.F. A study of a class of weighted bootstraps for censored data. Ann. Statist. 25 (1997) 1595-1621
18. Johnson, N.L., Kotz, S., Balakrishnan, N., 1994. Continuous Univariate Distributions, vol. 1. Wiley, New York.
19. Körner R., and Näther W. On the variance of random fuzzy variables. In: Bertoluzza C., Gil M.A., and Ralescu D.A. (Eds). Statistical Modeling Analysis and Management of Fuzzy Data (2002), Physica-Verlag, Heidelberg 22-39
20. Kudō H. Dependent experiments and sufficient statistics. Natl. Sci. Rep. Ochanomizu Univ. 4 (1954) 151-163
21. Kulpa Z. Diagrammatic representation for interval arithmetic. Linear Algebra Appl. 324 (2001) 55-80
22. Lima Neto E.A., De Carvalho F.A.T., and Tenorio C.P. Univariate and multivariate linear regression methods to predict interval-valued features. In: Webb G.I., and Xinghuo (Eds). Proceedings of the 17th Australian Joint Conference on Artificial Intelligence, AI 2004, Cairns, Australia, Lectures Notes on Artificial Intelligence vol. 3339 (2004), Springer, Heidelberg 526-537
23. Lyashenko N.N. The statistics of random compacts in the Euclidean space. Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 98 (1980) 115-139
24. Matheron G. Random Sets and Integral Geometry (1975), Wiley, New York
25. Molchanov I.S. Limit Theorems for Unions of Random Closed Sets. Lecture Notes in Mathematics (1993), Springer, Berlin
26. Molchanov I.S. Averaging of random sets and binary images. CWI Quart. 11 (1998) 371-384
27. Muirhead R.J. Aspects of Multivariate Statistical Theory (1982), Wiley, New York
28. Rao C.R. Linear Statistical Inference and Its Applications (1973), Wiley, New York
29. Serfling R.J. Approximation Theorems of Mathematical Statistics (1980), Wiley, New York