Imputation of missing values for compositional data using classical and robust methods

Computational Statistics and Data Analysis

Volumn 54, Issue 12, 2010, Pages 3095-3107

  Hron, K ^a   Templ, M ^b,c   Filzmoser, P ^b  

^a PALACKÝ UNIVERSITY   (Czech Republic)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^c Statistics Austria   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

MOTION COMPENSATION; NEAREST NEIGHBOR SEARCH; REGRESSION ANALYSIS;

IMPUTATION ALGORITHM; IMPUTATION METHODS; IMPUTATION OF MISSING VALUES; IMPUTATION TECHNIQUES; ITERATIVE REGRESSION; K-NEAREST NEIGHBORS; ROBUST REGRESSIONS; SIMULATED DATASETS;

ITERATIVE METHODS;

EID: 77955376324     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2009.11.023     Document Type: Article

References (32)

1. Aitchison, J., 1986. The Statistical Analysis of Compositional Data. Chapman & Hall, London, Reprinted in 2003 by Blackburn Press.
2. Aitchison, J., Barceló-Vidal, C., Martín-Fernández, J.A., Pawlowsky-Glahn, V., 2000. Logratio analysis and compositional distance. Mathematical Geology 32 (3), 271-275.
3. Beguin, C., Hulliger, B., 2008. The BACON-EEM algorithm for multivariate outlier detection in incomplete survey data. Survey Methodology 34 (1), 91-103.
4. Bishop, C.M., 1999. Probabilistic principal component analysis. Journal of the Royal Statistical Society, Series B 61, 611-622.
5. Bren, M., Tolosana-Delgado, R., van den Boogaart, K.G., 2008. News from "Compositions'', the R Package. CoDaWork'08. Girona. http://dugi-doc.udg. edu/bitstream/10256/716/1/BREN-cw08-nfc.pdf.
6. Dempster, A.P., Laird, N.M., Rubin, D.B., 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society 39, 1-38.
7. Egozcue, J.J., Pawlowsky-Glahn, V., 2005. Groups of parts and their balances in compositional data analysis. Mathematical Geology 37 (7), 795-828.
8. Egozcue, J.J., Pawlowsky-Glahn, V., 2006. Simplicial geometry for compositional data. In: Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (Eds.), Compositional Data Analysis in the Geosciences: From Theory to Practice. In: Special Publications, vol. 264. Geological Society, London, pp. 145-160.
9. Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueraz, G., Barceló-Vidal, C., 2003. Isometric logratio transformations for compositional data analysis. Mathematical Geology 35 (3), 279-300. (Pubitemid 38149265)
10. Filzmoser, P., Hron, K., 2008. Outlier detection for compositional data using robust methods. Mathematical Geosciences 40 (3), 233-248.
11. Filzmoser, P., Hron, K., 2009. Correlation analysis for compositional data. Mathematical Geosciences 41 (8), 905-919.
12. Filzmoser, P., Hron, K., Reimann, C., 2009. Principal component analysis for compositional data with outliers. Environmetrics 20 (6), 621-632.
13. Fritz, H., Filzmoser, P., 2008. Plausibility of Databases and the Relation to Imputation Methods. VDM Verlag Dr. Müller, Saarbrücken, ISBN: 978-3-8364-5992-1.
14. Kim, H., Golub, G.H., Park, H., 2005. Missing value estimation for DNA microarray gene expression data: Local least squares imputation. Bioinformatics 21 (2), 187-198. (Pubitemid 40202020)
15. Kovács, L.Ó., Kovács, G.P., Martín- Fernández, J.A., Barceló-Vidal, C., 2006. Major-oxide compositional discrimination in Cenozoic volcanites of Hungary. In: Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (Eds.), Compositional Data Analysis in the Geosciences: From Theory to Practice. In: Special Publications, vol. 264. Geological Society, London, pp. 145-160.
16. Little, R.J.A., Rubin, D.B., 2002. Statistical Analysis with Missing Data, second ed. Wiley, New Jersey.
17. Maronna, R., Martin, R.D., Yohai, V.J., 2006. Robust Statistics: Theory and Methods. John Wiley, New York.
18. Martín-Fernández, J.A., Barceló-Vidal, C., Pawlowsky-Glahn, V., 2003. Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Mathematical Geology 35 (3), 253-278. (Pubitemid 38154074)
19. Mateu-Figueras, G., Pawlowsky-Glahn, V., 2008. A critical approach to probability laws in geochemistry. Mathematical Geosciences 40 (5), 489-502.
20. Oba, S., Sato, M.A., Takemasa, I., Monden, M., Matsubara, K., Ishii, S., 2003. A Bayesian missing value estimation method for gene expression expression profile data. Bioinformatics 19 (16), 2088-2096. (Pubitemid 37408160)
21. Palarea-Albaladejo, J., Martín-Fernández, J.A., 2008. A modified EM alr-algorithm for replacing rounded zeros in compositional data sets. Computer & Geosciences 34 (8), 902-917.
22. Pawlowsky-Glahn, V., Egozcue, J.J., 2002. BLU estimators and compositional data. Mathematical Geology 34 (3), 259-274.
23. Pawlowsky-Glahn, V., Egozcue, J.J., Tolosana-Delgado, J., 2007. Lecture notes on compositional data analysis. http://hdl.handle.net/10256/297.
24. Pearson, K., 1897. 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, 489-502.
25. Rousseeuw, P.J., Van Driessen, K., 2006. Computing LTS regression for large data sets. Data Mining and Knowledge Discovery 12, 29-45. (Pubitemid 43255930)
26. R Development Core Team. 2008. R: A language and environment for statistical computing. Vienna. http://www.r-project.org.
27. Schafer, J.L., 1997. Analysis of Incomplete Multivariate Data. Chapman & Hall, London.
28. Scholz, M., Kaplan, F., Guy, C.L., Kopka, J., Selbig, J., 2005. Non-linear PCA: A missing data approach. Bioinformatics 21, 3887-3895. (Pubitemid 41535504)
29. Serneels, S., Verdonck, T., 2008. Principal component analysis for data containing outliers and missing elements. Computational Statistics & Data Analysis 52 (3), 1712-1727. (Pubitemid 350007799)
30. Troyanskaya, O., Cantor, M., Sherlock, G., Brown, P., Hastie, T., Tibshirani, R., Botstein, D., Altman, R., 2001. Missing value estimation methods for DNA microarrays. Bioinformatics 17 (6), 520-525. (Pubitemid 32600498)
31. Van den Boogaart, K.G., Tolosana-Delgado, R., Bren, M., 2006. Concept for handling with zeros and missing values in compositional data. In: Proceedings of IAMG'06-The XI Annual Conference of the International Association for Mathematical Geology. University of Liege, Belgium. CD-ROM.
32. Yucel, R.M., Demirtas, H., 2010. Impact of non-normal random effects on inference by multiple imputation: A simulation assessment. Computational Statistics & Data Analysis 54 (3), 790-801.