🚀 go-pugleaf

Colloquium - Department of Statistics, University of Toronto

Topic:     Decision Rule for Dimension in the Context of Manova
Speaker:   Prof. J.K. Ghosh
	   Purdue University and Indian Statistical Institute
Date:      Thursday, November 26    4:00 - 5:00
Place:     Room 1073, Sidney Smith Hall, 100 St. George Street
Abstract:

In the context of Multivariate Analysis of Variance (MANOVA), it is 
of interest to know the dimension of the space generated by the population
mean vectors centered at zero.  This would help identification of a 
structural relation, if there is any.  Formally, we have p normal
populations each of dimension  d, p > d.  Let the mean vectors be 
mu sub 1, ..., mu sub p and omega the common disperson matrix.

Let M = (mu sub 1 - mu bar, mu sub 2 - mu bar, ..., mu sub p - mu bar) 
where mu bar = p sup -1 SIGMA sub {mu i}.  We have actions or decisions 
a sub 0, ..., a sub d, where a sub i is the decision M has rank i.

We propose an intuitively appealing ad hoc rule, then show it is close to
being Bayes for a suitable prior and finally refine the ad hoc rule in
the light of the Bayes rule.  Its performance is studied in the frequentist 
paradigm.  We also report briefly on ongoing work with Rahul Mukerjee on 
construction of reference and other non-informative priors and their use
in a Bayesian treatment of this problem.  We focus on the case of known 
OMEGA and d = 2, but indicate what is to be done for general
d and unknown OMEGA $.  (This work is joint with Anindya De).
________________________________________________________________________________
Coffee, Tea and Cookies will be served in the Delury Lounge (SS6004) at 3:30 p.m.