Publications

Jay H. Beder
Department of Mathematical Sciences
University of Wisconsin-Milwaukee

JHB and Jeb F. Willenbring, "Invariance of generalized wordlength patterns", Journal of Statistical Planning and Inference, to appear. Available at arXiv.org .
Xu and Wu (2001) defined the generalized wordlength pattern (GWLP) of a design by indexing the levels of each factor by a cyclic group. When the number of levels of a factor is composite, other choices of abelian group are possible. We show that the GWLP is independent of this choice, although the so-called J-characteristics (defined by Ai and Zhang, 2004) are not.
JHB and Richard Gomulkiewicz, "Optimizing selection for function-valued traits", Journal of Mathematical Biology 55:861--882, 2007 ; in dvi , ps (postscript), or pdf format.
This is the third in a series, following Beder&Gomulkiewicz (1998) below. We compute the selection differential and (especially) the selection gradient for a Gaussian trait with a "Gaussian" fitness function that models optimizing selection. The paper relies in part on Lukic&Beder (2001).
JHB, "Main effects". In Encyclopedia of Statistics in Quality and Reliability, F. Ruggeri, R. Kenett, and F. W. Faltin, eds., pages 990--993. John Wiley & Sons, Ltd., Chichester, UK, 2007.
JHB, "On the definition of effects in fractional factorial designs", Utilitas Mathematica 66:47-60, 2004; in dvi , ps (postscript), or pdf format.
This is a follow-up to the paper, "On Rao's inequalities for arrays of strength d," below, but with a simpler approach. It includes a couple of applications to aliasing in non-regular fractions.
Wiebke S. Diestelkamp and JHB. On the decomposition of orthogonal arrays. Utilitas Mathematica, 61:65-86, 2002. (MR 2003i:05029)
JHB. Aspects of Fortet's work on reproducing kernel Hilbert spaces. In Écrits sur les Processus Aléatoires: Mélanges en Hommage à Robert Fortet Robert Fortet, M. Brissaud, ed., Hermès, Paris. 2002, pages 91-102.
The article reviews two papers of Fortet and some related results, but Section 3 of the published version is rather out of date. An updated (unpublished) version is available online in dvi , ps (postscript), or pdf format. Section 3 summarizes results from Lukic and Beder (2001) below.
Milan N. Lukic and JHB. Stochastic processes with sample paths in reproducing kernel Hilbert spaces. Transactions of the American Mathematical Society, 353:3945-3969, 2001.
JHB and Richard Gomulkiewicz. Computing the selection gradient and evolutionary response of an infinite-dimensional trait. Journal of Mathematical Biology, 36:299-319, 1998. (MR 99f: 92009).
This is a follow-up of Gomulkiewicz and Beder (1996) below, and includes (among other things) the rigorous development for infinite-dimensional traits of the so-called Breeder's Equation. Applications show how to compute gradients.
JHB. On Rao's inequalities for arrays of strength d. Utilitas Mathematica, 54:85-109, 1998.
JHB. Conjectures about Hadamard matrices. Journal of Statistical Planning and Inference, 72:7-14, 1998. Erratum, 84:343, 2000.
Richard Gomulkiewicz and JHB. The selection gradient of an infinite-dimensional trait. SIAM Journal of Applied Mathematics, 56:509-523, 1996. (MR 97e: 92004).
This gives a rigorous development of the modeling of infinite-dimentional traits, in particular the selection differential and selection gradient. Lost in the biology is an interesting (to me) "derivative" which (I think) may be useful in other applications: The functional gradient of E_m(W), where m is the mean of a Gaussian process and W is a function of the process. (The analog in multivariate analysis would be the directional derivative of E(W) with respect to the mean vector.)
JHB and Robert C. Heim. On the use of ridit analysis. Psychometrika, 55:603-616, 1990. Erratum, 57:160, 1992.
JHB. The problem of confounding in two-factor experiments. Communications in Statistics: Theory and Methods, A18:2165-2188, 1989. Correction, A23(7), 2131-2132, 1994. (MR 90g: 62189; 90m: 26188).
Anestis Antoniadis and JHB. Joint estimation of the mean and the covariance of a Banach valued Gaussian vector. Statistics, 20:77-93, 1989. (MR 90k: 62183).
JHB. A sieve estimator for the covariance of a Gaussian process. Annals of Statistics, 16:648-660, 1988. (MR 89f: 62073).
JHB. Estimating a covariance function having an unknown scale parameter. Communications in Statistics: Theory and Methods, A17:323-340, 1988. (MR 89j: 62118).
JHB. A sieve estimator for the mean of a Gaussian process. Annals of Statistics, 15:59-78, 1987. (MR 88f: 62124).
Marc Mangel and JHB. Search and stock depletion: Theory and applications. Canadian Journal of Fisheries and Aquatic Sciences, 42:150-163, 1985.
JHB. Likelihood methods for Gaussian processes. PhD thesis, The George Washington University, 1981.
I mention this mainly because the title scans in perfect dactylic tetrameter. However, the contents were not without value. The only paper that comes directly out of the dissertation is the "Estimating ... unknown scale parameter" (1988). But the material became the foundation for the two main sieve papers (Ann. Statist., 1987 and 1988).