Model-based replacement of rounded zeros in compositional data: Classical and robust approaches

Computational Statistics and Data Analysis

Volumn 56, Issue 9, 2012, Pages 2688-2704

  Martn Fernndez, J A ^a   Hron, K ^b   Templ, M ^c,d   Filzmoser, P ^c   Palarea Albaladejo, J ^e  

^a UNIVERSITY OF GIRONA   (Spain)

^b PALACKÝ UNIVERSITY   (Czech Republic)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^d Statistics Austria ^*  (Austria)

^e BIOMATHEMATICS AND STATISTICS SCOTLAND   (United Kingdom)

Author keywords

Balances; EM algorithm; Log ratio transformations; Robust regression; Values below detection limit

Indexed keywords

CENSORED REGRESSION; COMPOSITIONAL DATA; DETECTION LIMITS; EM ALGORITHMS; GEOCHEMICAL DATA; REGRESSION METHOD; ROBUST APPROACHES; ROBUST METHODS; ROBUST REGRESSIONS;

ALGORITHMS; MONTE CARLO METHODS; PRECISION BALANCES;

REGRESSION ANALYSIS;

EID: 84859903807     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2012.02.012     Document Type: Article

References (36)

1. J. Aitchison The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability 1986 Chapman and Hall Ltd. London, UK p. 416 (Reprinted 2003 with additional material by The Blackburn Press)
2. J. Aitchison, C. Barceló-Vidal, J.A. Martn-Fernndez, and V. Pawlowsky-Glahn Logratio analysis and compositional distance Mathematical Geology 32 3 2000 271 275
3. T. Amemiya Tobit models: a survey Journal of Econometrics 24 1984 3 61
4. Barceló-Vidal, C.; Aguilar, L.; Martn-Fernndez, J.A.; 2011. Compositional VARIMA Time Series (Chapter 7). In: Pawlowsky-Glahn and Buccianti (2011), pp. 87-103.
5. A. Buccianti, G. Mateu-Figueras, and V. Pawlowsky-Glahn Compositional Data Analysis in the Geosciences: From Theory to Practice Special Publications vol. 264 2006 Geological Society London
6. Daunis-i-Estadella, J.; Martn-Fernndez, J.A. (Eds.), 2008. Proceedings of CODAWORK'08, the 3rd Compositional Data Analysis Workshop. Universitat de Girona. ISBN: 84-8458-272-4. http://ima.udg.es/Activitats/CoDaWork08/, May 27-30 (CD-ROM).
7. J.J. Egozcue Reply to on the harker variation diagrams; by J.A. Cortés Mathematical Geosciences 41 7 2009 829 834
8. J.J. Egozcue, and V. Pawlowsky-Glahn Groups of parts and their balances in compositional data analysis Mathematical Geology 37 7 2005 795 828
9. J.J. Egozcue, and V. Pawlowsky-Glahn Simplicial geometry for compositional data A. Buccianti, G. Mateu-Figueras, V. Pawlowsky-Glahn, Compositional Data Analysis in the Geosciences: From Theory to Practice Special Publications vol. 264 2006 Geological Society London 145 160
10. Egozcue, J.J.; Pawlowsky-Glahn, V.; 2011. Basic concepts and procedures (Chapter 2). In: Pawlowsky-Glahn and Buccianti (2011), pp. 12-28.
11. J.J. Egozcue, V. Pawlowsky-Glahn, G. Mateu-Figueras, and C. Barceló-Vidal Isometric logratio transformations for compositional data analysis Mathematical Geology 35 3 2003 279 300
12. Egozcue, J.J.; Tolosana-Delgado, R.; Ortego, M.I. (Eds.), 2011. Proceedings of CODAWORK'11, the 4th Compositional Data Analysis Workshop. Sant Feliu De Guxols. ISBN: 978-84-87867-76-7 (electronic publication). May 10-13.
13. P. Filzmoser, and K. Hron Outlier detection for compositional data using robust methods Mathematical Geosciences 40 3 2008 233 248
14. Filzmoser, P.; Hron, K.; 2011. Robust statistical analysis (Chapter 5). In: Pawlowsky-Glahn and Buccianti (2011), pp. 59-72.
15. P. Filzmoser, K. Hron, and C. Reimann Principal component analysis for compositional data with outliers Environmetrics 20 6 2009 621 632
16. E. Fišerov, and K. Hron On interpretation of orthonormal coordinates for compositional data Mathematical Geosciences 43 4 2011 455 468
17. K. Hron, M. Templ, and P. Filzmoser Imputation of missing values for compositional data using classical and robust methods Computational Statistics and Data Analysis 54 12 2010 3095 3107
18. P.J. Huber Robust Statistics 1981 John Wiley New York
19. R.A. Johnson, and D.W. Wichern Applied Multivariate Statistical Analysis fifth ed. 2002 Prentice Hall London
20. R.J.A. Little, and D.B. Rubin Statistical Analysis with Missing Data second ed. 1987 Wiley New Jersey
21. R. Maronna, R.D. Martin, and V.J. Yohai Robust Statistics: Theory and Methods 2006 John Wiley New York, USA p. 436
22. J.A. Martn-Fernndez, C. Barceló-Vidal, and V. Pawlowsky-Glahn Dealing with zeros and missing values in compositional data sets using nonparametric imputation Mathematical Geology 35 3 2003 253 278
23. Martn-Fernndez, J.A.; Palarea-Albaladejo, J.; Olea, R.A.; 2011. Dealing with zeros (Chapter 4). In: Pawlowsky-Glahn and Buccianti (2011), pp. 47-62.
24. J.A. Martn-Fernndez, and S. Thió-Henestrosa Rounded zeros: some practical aspects for compositional data A. Buccianti, G. Mateu-Figueras, V. Pawlowsky-Glahn, Compositional Data Analysis in the Geosciences: From Theory to Practice Special Publications vol. 264 2006 Geological Society London 191 201
25. Mateu-Figueras, G.; Barceló-Vidal, C. (Eds).; 2005. Proceedings of CODAWORK'05, the 2nd Compositional Data Analysis Workshop. Universitat de Girona. ISBN: 84-8458-222-1. http://ima.udg.es/Activitats/CoDaWork05/, October 19-21 (CD-ROM).
26. G. Mateu-Figueras, and V. Pawlowsky-Glahn A critical approach to probability laws in geochemistry Mathematical Geosciences 40 5 2008 489 502
27. J. Palarea-Albaladejo, and J.A. Martn-Fernndez A modified EM alr-algorithm for replacing rounded zeros in compositional data sets Computers & Geosciences 34 8 2008 902 917
28. J. Palarea-Albaladejo, J.A. Martn-Fernndez, and J. Gómez-Garca A parametric approach for dealing with compositional rounded zeros Mathematical Geology 39 7 2007 625 645
29. V. Pawlowsky-Glahn, and A. Buccianti Compositional Data Analysis: Theory and Applications 2011 John Wiley & Sons, Ltd. Chichester,UK 378
30. K. Pearson Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs Proceedings of the Royal Society of London 60 1897 489 502
31. R Development Core Team, 2008. R: a language and environment for statistical computing. Vienna. http://www.r-project.org.
32. C. Reimann, M. yrs, V.A. Chekushin, I. Bogatyrev, R. Boyd, P. de Caritat, R. Dutter, T.E. Finne, J.H. Halleraker, Ø Jæger, G. Kashulina, H. Niskavaara, O. Lehto, V. Pavlov, M.L. Risnen, T. Strand, and T. Volden Environmental Geochemical Atlas of the Central Barents Region 1998 NGU-GTK-CKE Special Publication Trondheim, Norway p. 745
33. C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter Statistical Data Analysis Explained: Applied Environmental Statistics with R 2008 Wiley Chichester
34. G.A.F. Seber A Matrix Handbook for Statisticians 2008 John Wiley & Sons, Inc. Hoboken, New Jersey, USA p. 559
35. Thió-Henestrosa, S. Martn-Fernndez, J.A. (Eds.), 2003. Proceedings of CODAWORK'03, the 1st Compositional Data Analysis Workshop. Universitat de Girona. ISBN: 84-8458-111-X. http://ima.udg.es/Activitats/CoDaWork03/, October 15-17 (CD-ROM).
36. Tolosana-Delgado, R.; van den Boogaart, K.G.; Pawlowsky-Glahn, V.; 2011. Geostatistics for compositions (Chapter 6). In: Pawlowsky-Glahn and Buccianti (2011), pp. 73-86.