On projection-based tests for directional and compositional data

Statistics and Computing

Volumn 19, Issue 4, 2009, Pages 367-380

  Cuesta Albertos, Juan A ^a   Cuevas, Antonio ^b   Fraiman, Ricardo ^c,d  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSIDAD DE SAN ANDRÉS   (Argentina)

^d UNIVERSIDAD DE LA REPÚBLICA   (Uruguay)

Author keywords

Compositional data; Directional data; Sphericity; Uniformity

Indexed keywords

EID: 70450286411     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-008-9098-3     Document Type: Article

References (27)

1. Aitchison, J.: The Statistical Analysis of Compositional Data. Chapman and Hall, London (1986)
2. Aitchison, J., Egozcue, J.J.: Compositional data analysis: Where are we and where should we be heading? Math. Geol. 37, 829-850 (2005)
3. Berk, R.H., Jones, D.H.: Relatively optimal combinations of tests statistics. Scand. J. Stat. 5, 158-162 (1978)
4. Brown, T.C., Cartwright, D.I., Eagleson, G.K.: Correlations and characterizations of the uniform distribution. Aust. J. Stat. 28, 89-96 (1986)
5. Cuesta-Albertos, J.A., Fraiman, R., Ransford, T.: Random projections and goodness-of-fit tests in infinite-dimensional spaces. Bull. Braz. Math. Soc. 37, 1-25 (2006)
6. Cuesta-Albertos, J.A., del Barrio, T., Fraiman, R., Matrán, C.: The random projection method in goodness of fit for functional data. Comput. Stat. Data Anal. 51, 4814-4831 (2007a)
7. Cuesta-Albertos, J.A., Fraiman, R., Ransford, T.: A sharp form of the Cramer-Wold theorem. J. Theor. Probab. 20, 201-209 (2007b)
8. Cuevas, A., Fraiman, R.: On depth measures and dual statistics: A methodology for dealing with general data. J. Multivariate Anal. (2008, to appear)
9. Fang, K.T., Kotz, S.K., Ng, K.W.: Symmetric Multivariate and Related Distributions. Chapman & Hall, London (1990)
10. Figueiredo, A.: Comparison of tests of uniformity defined on the hypersphere. Stat. Probab. Lett. 77, 329-334 (2007)
11. Fisher, N.I.: Statistical Analysis of Circular Data. Cambridge University Press, Cambridge (1993)
12. Giné, E.: Invariant tests for uniformity on compact Riemannian manifolds based on Sobolev norms. Ann. Stat. 3, 1243-1266 (1975)
13. Juan, J., Prieto, F.J.: Using angles to identify concentrated multivariate outliers. Technometrics 43, 311-322 (2001)
14. Jupp, P.E., Kim, P.T., Koo, J.Y., Wiegert, P.: The intrinsic distribution and selection bias of long-period cometary orbits. J. Am. Stat. Assoc. 98, 515-521 (2003)
15. Lattin, J., Carroll, J.D., Green, P.E.: Analyzing Multivariate Data. Brooks/Cole, Pacific Grove (2003)
16. Lund, U., Agostinelli, C.: Circular: Circular Statistics. R package version 0.3-6 (2006)
17. Mardia, K.V., Jupp, P.E.: Directional Statistics. Wiley, Chichester (2000)
18. Marsden, B.G., Williams, G.V.: Catalogue of Cometary Orbits, 8th edn. Minor Planet Center, Smithsonian Astrophysical Observatory, Cambridge (1993)
19. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2006). ISBN 3-900051-07-0, URL http://www.R-project.org
20. Shohat, J.A., Tamarkin, J.D.: The Problem of Moments. Am. Math. Soc., Providence (1943)
21. Stephens, M.A.: Use of the von Mises distribution to analyse continuous proportions. Biometrika 69, 197-203 (1982)
22. Teets, D.A., Whitehead, K.: Computation of planetary orbits. College Math. J. 29, 397-404 (1998)
23. Timm, N.H.: Applied Multivariate Analysis. Springer, New York (2002)
24. Ulrich, G.: Computer generation of distributions on the m-sphere. Appl. Stat. 33, 158-163 (1984)
25. van den Boogaart, K.G., Tolosana, R., Bren, M.: Compositions: Compositional Data Analysis. R package version 0.91-6, URL: http://www.stat.boogaart.de/compositions (2006)
26. Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S, 4th edn. Springer, New York (2002)
27. Wood, A.T.A.: Simulation of the von Mises-Fisher distribution. Commun. Stat. Simul. Comput. 23(1), 157-164 (1994)