SPEAKER: |
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TITLE: |
"Geometry of multivariate normal distributions" |
DAY: |
Wednesday, January 26, 2000 |
TIME: |
3:30 p.m. [Coffee & cookies in BSB-202 at 3:00 p.m.] |
PLACE: |
BSB-108 |
Geometric methods have been used by a number of statisticians in parametric inference problems. The Fisher information matrix defines a Riemannian metric on the parameter space and geometric (i.e. coordinate independent) properties of the model can be studied. The two main models used are exponential families and transformational families with symmetries. In this talk we will concentrate on transformational models. After a brief but general introduction to some of the differential-geometric ideas used in parametric estimation, we will discuss the following topics:
If time permits, we will also give a short account of random matrix theory and its relation to the Wishart distribution.
One goal of this talk is to show that there is a link between differential geometry and certain aspects of multivariate statistics.
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Dr Maung Min-Oo obtained his B.Sc. from Rangoon University in Burma and his Dip. Math. and Dr. rer. nat. from Bonn University in Germany. He is Professor in the Department of Mathematics & Statistics at McMaster University. His interests include Differential Geometry, Geometric Analysis, General Relativity, and Financial Mathematics.
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The references below have been suggested by Dr Min-Oo as useful background for his talk. Papers [1] and [2] have been placed on reserve at Thode Library (STATS 770: Statistics Seminar).
Papers:
[1] M.Lovric, M.Min-Oo and E.Ruh: "Multivariate normal distributions parametrized as a Riemannian symmetric space"; preprint, McMaster University, 1998. (submitted to J. Multivariate Analysis).
[2] P.Bougerol: "Kalman filtering with random coefficients and contractions"; SIAM J. Control and Optimization vol.31.4, pp. 942-959, 1993.
[3] M.Calvo and J.M.Oller: "A distance between multivariate normal distributions based on an embedding into the Siegel group", J. Multivariate Analysis vol.35, pp. 223-242, 1990.
[4] L.T.Skovgaard: "A Riemannian geometry of the multivariate normal model"; Scand. J. Statistics vol.11, pp. 211-223, 1984.
Books:
[1] O.E.Barndorff-Nielsen: Parametric statistical models and likelihood, Lecture Notes in Statistics #50, Springer-Verlag, 1988.
[2] M.K.Murray and J.W.Rice: Differential Geometry and Statistics, Monographs on Statistics and Applied Probability, Chapman and Hall, 1993.
[3] A.V.Balakrishnan: Kalman filtering theory, Optimization Software Inc., 1984.