601 research outputs found
William H. Kruskal and the Development of Coordinate-Free Methods
Discussion of ``The William Kruskal Legacy: 1919--2005'' by Stephen E.
Fienberg, Stephen M. Stigler and Judith M. Tanur [arXiv:0710.5063]Comment: Published in at http://dx.doi.org/10.1214/088342306000000367 the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A maximization problem and its application to canonical correlation
AbstractLet Σ be an n × n positive definite matrix with eigenvalues λ1 ≥ λ2 ≥ … ≥ λn > 0 and let M = {x, y | x ϵ Rn, y ϵ Rn, x ≠0, y ≠0, x′y = 0}. Then for x, y in M, we have that x′Σy(x′Σxy′Σy)12 ≤ (λ1 − λn)(λ1 + λn) and the inequality is sharp. If ∑=∑11∑12∑21∑22 is a partitioning of Σ, let θ1 be the largest canonical correlation coefficient. The above result yields θ1 ≤ (λ1 − λn)(λ1 + λn)
Dutch book in simple multivariate normal prediction: Another look
In this expository paper we describe a relatively elementary method of
establishing the existence of a Dutch book in a simple multivariate normal
prediction setting. The method involves deriving a nonstandard predictive
distribution that is motivated by invariance. This predictive distribution
satisfies an interesting identity which in turn yields an elementary
demonstration of the existence of a Dutch book for a variety of possible
predictive distributions.Comment: Published in at http://dx.doi.org/10.1214/193940307000000356 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Evaluation of Formal posterior distributions via Markov chain arguments
We consider evaluation of proper posterior distributions obtained from
improper prior distributions. Our context is estimating a bounded function
of a parameter when the loss is quadratic. If the posterior mean of
is admissible for all bounded , the posterior is strongly
admissible. We give sufficient conditions for strong admissibility. These
conditions involve the recurrence of a Markov chain associated with the
estimation problem. We develop general sufficient conditions for recurrence of
general state space Markov chains that are also of independent interest. Our
main example concerns the -dimensional multivariate normal distribution with
mean vector when the prior distribution has the form on the parameter space . Conditions on for strong
admissibility of the posterior are provided.Comment: Published in at http://dx.doi.org/10.1214/07-AOS542 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A condition for null robustness
AbstractSufficient conditions are given that certain statistics have a common distribution under a wide class of underlying distributions. Invariance methods are the primary technical tool in establishing the theoretical results. These results are applied to MANOVA problems, problems involving canonical correlations, and certain statistics associated with the complex normal distribution
A Maximization Problem and its Application to Canonical Correlation
1 online resource (PDF, 9 pages
A Probability Inequality for Linear Combinations of Bounded Random Variables
1 online resource (PDF, 10 pages
Orderings Induced on Rn By Compact Groups of Linear Transformations with Applications to Probability Inequalities (Preliminary Report)
1 online resource (PDF, 19 pages
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