- JHB and Margaret Ann McComack, “A note on the minimum size of an orthogonal array”, 2015, to appear in Communications in Statistics: Theory and Methods. Available at arXiv.org .
- JHB and Jesse S. Beder, “Generalized wordlength patterns and strength”, Journal of Statistical Planning and Inference, 144C: 41-46, 2014. Available at arXiv.org .
- JHB and Wiebke S. Diestelkamp, “Box-Hunter resolution in nonregular fractional factorial designs”, Journal of Statistical Theory and Practice, 3(4), 879–889, December 2009. Available at arXiv.org.
The main result (Theorem 3.7) asserts that for an arbitrary (simple) fraction, maximum resolution = 1 + maximum strength. The 2004 paper in Utilitas (below) only asserted ≥. No use is made of wordlengths, but rather just the Box-Hunter definition of resolution.
- JHB and Jeb F. Willenbring, “Invariance of generalized wordlength patterns”, Journal of Statistical Planning and Inference, 139(8): 2706-2714, 1 August 2009. 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 ps (postscript), and 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 ps (postscript), and 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. 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.
None of the conjectures of this paper panned out.The conjecture on complex Hadamard matrices was known to be incorrect at the time I wrote the paper, as pointed out to me by Prof. C. H. Cooke. A corrected version of the paper was actually accepted by the editor of that special issue of JSPI before it went to press, but for reasons that I was unable to ascertain the uncorrected version is the one that was published. Hence the Erratum. I was also required to eliminate from the Erratum any reference to editorial error.
When the uncorrected version appeared, Prof. Cooke published a note on the subject ( MR — 2001a:05026 ).
The remaining conjectures of this paper have been disproved by a more extensive computer search than I was able to do at the time. See Dursun A. Bulutoglu, David M. Kaziska, A counterexample to Beder’s conjectures about Hadamard matrices, JSPI, 139(9), 2009, 3381-3383.
- 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).
Discussions and Miscellaneous Publications
JHB. Claims about Torah codes are false and prove nothing. Wisconsin Jewish Chronicle, Section 2, April 10, 1998, pages 15-17. Reviews the mathematical and textual objections to so-called Bible codes.
Discussion of paper by Peter McCullagh, Invariance and factorial models, Journal of the Royal Statistical Society, B, 62:246-247, 2000.
Simultaneous diagonalization of two covariance kernels. Technical Report No. 4 (1992-93), Dept. of Mathematical Sciences, UWM. (Original ms., 1987.)