Hilbert space of probability density functions based on aitchison geometry

Acta Mathematica Sinica, English Series

Volumn 22, Issue 4, 2006, Pages 1175-1182

  Egozcue, J J ^a   Diaz Barrero J L ^a   Pawlowsky Glahn V ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF GIRONA   (Spain)

Author keywords

Aitchison distance; Bayes' theorem; Fourier coefficients; Haar basis; Least squares approximation; Simplex

Indexed keywords

EID: 33746389740     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-005-0678-2     Document Type: Article

References (12)

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2. Aitchison, J., The Statistical Analysis of Compositional Data: Monographs on Statistics and Applied Probability, Chapman & Hall Ltd., London (UK), 1986, (Reprinted in 2003 with additional material by The Blackburn Press)
3. Billheimer, D., Guttorp, P., Fagan, W. F.: Statistical Interpretation of Species Composition. Journal of the American Statistical Association, 96, 1205-1214 (2001)
4. Pawlowsky-Glahn, V., Egozcue, J. J.: Geometric approach to statistical analysis on the simplex. Stochastic Enviromental Research and Risk Assessment, 15, 384-398 (2001)
5. Pawlowsky-Glahn, V., Egozcue, J. J.: BLU Estimators and Compositional Data. Mathematical Geology, 34, 259-274 (2002)
6. Aitchison, J., Barceló-Vidal, C., Egozcue, J. J., Pawlowsky-Glahn, V.: A concise guide to the algebraic-geometric structure of the simplex, the sample space for compositional data analysis, Proceedings of IAMG'02, The Seventh Annual Conference of the International Association for Mathematical Geology, Berlin, Germany, 2002
7. Burbea, J., Rao, R.: Entropy differential metric, distance and divergence measures in probability spaces: aunifled approach. Journal of Multivariate Analysis, 12, 575-596 (1982)
8. Egozcue, J. J., Díaz-Barrero, J. L.: Hilbert space of probability density functions with Aitchison geometry, Proceedings of Compositional Data Analysis Workshop, CoDaWork'03, Girona (Spain) 2003, (ISBN 84-8458-111-X)
9. Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barceló-Vidal, C.: Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35, 279-300 (2003)
10. Berberian, S. K.: Introduction to Hilbert Space, University Press, New York, 1961
11. Haar, A.: Zur Theorie der Ortogonalen Funktionen-Systeme. Math. Ann., 69, 331-371 (1910)
12. Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions, Dover, New York, 1972