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STATISTIQUE: analyse multidimensionnelle, théorie de la décision statistique, méthodes asymptotiques.




Martin BILODEAU            David BRENNER
Theory of Multivariate Statistics
Springer Texts in Statistics (Advisors: G. Casella, S. Fienberg and I. Olkin)
Springer-Verlag, 1999
xviii pages and 288 pages
ISBN 0-387-98739-8

This book presents the main results of the modern theory of multivariate statistics to those who would appreciate a concise and
 mathematically rigorous treatment.  Supplemented by over 140 problems, it can be used as a textbook by students taking a first
 graduate course. It will also serve as a general reference for research workers who will find, in a readable form, developments
 from recently published work on certain broad topics not otherwise easily accesible. These topics include robust inference
 and the bootstrap in a multivariate setting.

 The treatment is in most ways thoroughly orthodox, but in several ways novel and unique. The approach taken rests heavily on
 the essentially physical notion of equality-in-distribution and makes vigorous use of the Cramér-Wold theorem.  In this way, it
 is much more structural and directly algebraic than is usual, tied more immediately to the way in which statistical objects arise in
 nature, practice or computational simulation.  Readers should find the approach refreshing, even perhaps liberating, particularly
 those saturated in a lifetime of matrix derivatives and jacobians.

 As a textbook, the first eight chapters provide more than enough material for coverage in one semester.  The remaining six chapters
 treat of more specialized topics: multivariate regression, principal components and canonical correlations, asymptotic expansion,
 robustness and the bootstrap, taking the reader gradually into territory not altogether perfectly charted.  This should serve to draw
 one gently into the literature.

 Martin Bilodeau is professor in the department of mathematics and statistics at the Université de Montréal. He is an Associate of the 
Society of Actuaries. His research interests include statistical decision theory and multivariate statistics.

 David Brenner is professor of statistics in the department of statistics at the University of Toronto with over 25 years experience
as an educator. His research interests include statistical inference and multivariate statistical methods.


To order:

To download the file "multivariate" of S-Plus programs in Appendix C of the book press Shift and click simultaneously on the link Theory of Multivariate Statistics.

On peut télécharger le fichier "multivariate" de programmes S-Plus décrit dans l'appendice C du livre en pressant la touche Shift et en cliquant simultanément sur le lien Theory of Multivariate Statistics.




30. Bilodeau, M. (2021). Anova of Balanced Variance Component Models, arXiv:2103.13202v2, 1-8.

29. Bilodeau, M. and Guetsop Nangue, A. (2017). Tests of Mutual or Serial Independence of Random Vectors with Applications, Journal of Machine Learning Research, 18(74), 1-40. pdf dCov.R examples.R TEMPERAT.txt TSXComp.csv

28. Bilodeau, M., Lafaye de Micheaux, P, Mahdi, S. (2015). The R Package groc for Generalized Regression on Orthogonal Components, Journal of Statistical Software, 65(1), 1-29. pdf

27. Bilodeau, M. (2014). Graphical lassos for meta-elliptical distributions. Canadian Journal of Statistics. Canadian Journal of Statistics 42(2), 185-203, 2014. pdf

26. Bilodeau, M. (2013). Analysis of variance, multivariate (MANOVA) in Encyclopedia of Environmetrics Second Edition, A.-H. El-Shaarawi and W. Piegorsch (eds).  John Wiley & Sons Ltd,Chichester, UK, pp. 85-88. DOI: 10.1002/9780470057339.vnn075. pdf

25. Bilodeau, M., Hassan Zadeh, A. , Fitting bivariate losses with phase-type distributions. Scandinavian Actuarial Journal 2013(4), 241-262, 2013. pdf

24. Guénard, G., Legendre, P., Boisclair, D. and Bilodeau, M., Multiscale codependence analysis: an integrated approach to analyse relationships accross scales. Ecology 91, 2952-2964, 2010. pdf

23. Bilodeau, M. and Lafaye de Micheaux, P., A-dependence statistics for mutual and serial independence of categorical variables, J. Statist. Planning Inf. 139, 2407-2419, 2009. pdf

22. Beran, R., Bilodeau, M. and Lafaye de Micheaux, P., Nonparametric tests of independence between random vectors, J. Multivariate Anal. 98(9), 1805-1824, 2007. pdf

21. Bilodeau, M. and Lafaye de Micheaux, P., A multivariate empirical characteristic function test of independence with normal marginals. J. Multivariate Anal. 95(2), 345-369, 2005. pdf

20. Bilodeau, M., Discussion: Tail conditional expectations for elliptical distributions. North American Actuarial Journal 8(3),  118-123, 2004.

19. Bilodeau, M., Asymptotic distribution of the largest eigenvalue. Commun. Statist.-Sim. and Comp. 31(3), 357-373, 2002.

18. Bilodeau, M. and Duchesne, P.,  Principal component analysis from multivariate familial correlation matrix. J. Multivariate Anal. 82(2), 457-470, 2002 .

17. Bilodeau, M., Discussion: Robust estimation of the tail index of a Pareto distribution.  North American Actuarial Journal 5(3),  123-126, 2001.

16. Bilodeau, M. and Duchesne, P.,  Robust estimation of the SUR Model. Canad. Jour. Statist., 28 (2), 277-288, 2000. pdf

15. Bilodeau, M.,  Multivariate Flattening for better Predictions. Canad. Jour. Statist. 28 (1), 159-170, 2000.

14. Bilodeau, M. and Brenner, D., Theory of multivariate statistics. Springer Texts in Statistics, Springer-Verlag (ISBN 0-387-98739-8), xviii pages and 288 pages, 1999.

13. Bilodeau M.,  Estimating a multivariate treatment effect under a biased allocation rule. Commun. Statist.-Theory Meth. 26 (5), 1119-1124, 1997.

12. Bilodeau M., Some remarks on U(p;m,n) distributions. Stat. and Prob. Letters. 31 (1), 41-43, 1996.

11. Bilodeau M.,  Minimax estimators of the mean vector in normal mixed linear models. J. Multivariate Anal. 52 (1), 73-82, 1995.

10. Bilodeau M. and Kariya T.,  LBI Tests of independence in bivariate exponential distributions. Ann. Inst. Statist. Math. 46 (1), 127-136, 1994.

9. Bilodeau M.,  Fourier smoother and generalized additive model. Canad. Jour. Statist. 20 (3), 257-269, 1992.

8. Bilodeau M. and Srivastava M.S., Estimation of the eigenvalues of $\Sigma_1\Sigma_2^{-1}$.} J. Multivariate Anal. 41 (1), 1-13, 1992.

7. Bilodeau M., On the choice of the loss function in covariance estimation. Statistics & Decisions  8, 131-139, 1990.

6. Bilodeau M., On the monotone regression dependence for archimedian bivariate uniform. Comm. Statist.-Theory Meth. 18 (3), 981-988, 1989.

5. Srivastava M.S. and Bilodeau M., Stein estimation under elliptical distributions. J. Multivariate Anal. 28 (2), 247-259, 1989.

4. Bilodeau M. and Kariya T., Minimax estimators in the normal MANOVA model. J. Multivariate Anal. 28 (2), 260-270, 1989.

3. Bilodeau M. and Srivastava M.S., Estimation of the MSE matrix of the Stein estimator. Canad. Jour. Statist. 16 (2), 153-159, 1988.

2. Bilodeau M., On the simultaneous estimation of scale-parameters. Canad. Jour. Statist. 16 (2), 169-174, 1988.

1. Bilodeau M., Sur une représentation explicite des solutions optimales d'un programme linéaire. Canad. Math. Bull.  29 (4), 419-425, 1986.