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- W. BRYC
- 2005

For an arbitrary random vector (X,Y ) and an independent random variable Z it is shown that the maximum correlation coefficient between X and Y + λZ as a function of λ is lower semicontinuous everywhere and continuous at zero where it attains its maximum. If, moreover, Z is in the class of self-decomposable random variables, then the maximal correlation… (More)

- Katarzyna Bryc, Wlodek Bryc, Jack W Silverstein
- Theoretical population biology
- 2013

We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented in the data. We indicate that the power of the technique relies more on the number of individuals… (More)

Large deviation principles and related results are given for a class of Markov chains associated to the “leaves” in random recursive trees and preferential attachment random graphs, as well as the “cherries” in Yule trees. In particular, the method of proof, combining analytic and Dupuis-Ellis type path arguments, allows for an explicit computation of the… (More)

- WLODEK BRYC, VIRGIL PIERCE
- 2008

This is a seminar talk of February 13, 2008. 1. Wick’s theorem for R-valued normal vectors The following is known as Wick’s theorem. Theorem A (Wick [9]). If (X1, . . . , X2n) is multivariate normal with mean zero, then E(X1X2 . . . X2n) = ∑ V ∏ {j,k}∈V E(XjXk), where the sum is taken over all pair partitions V of {1, 2, . . . , 2n}.1 For example,… (More)

- Wlodek Bryc, Raouf Fakhfakh, Abdelhamid Hassairi
- J. Multivariate Analysis
- 2014

We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also investigate when the domain of means can be extended beyond the ”natural domain”.

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