Abstract: Divisible design graphs (DDG for short) have been recently defined by Kharaghani, Meulenberg and the second author as a generalization of (v, k, λ)-graphs. In this paper we give some new constructions of DDGs, most of them using Hadamard matrices and (v, k, λ)-graphs. For three...

In this article, I discuss the main approaches to resampling variance es- timation in complex survey data: balanced repeated replication, the jackknife, and the bootstrap. Balanced repeated replication and the jackknife are implemented in the Stata svy suite. The bootstrap for complex survey...

In this paper we consider experimental situations in which m 2-level factors are to be studied using a 2-level main effects plan where n runs are to be partitioned into b blocks of different sizes. For these experimental situations, methods of constructing type I optimal designs are given.

Deriving a formula, we show that an optimal moment design has the property that each treatment combination appears as equally often as possible. Modifying the definition of minimum aberration to restricted minimum aberration, we show that the word length pattern of a design is proportional to...

U-type designs and orthogonal Latin hypercube designs (OLHDs) have been used extensively for performing computer experiments. Both have good spaced filling properties in one-dimension. U-type designs may not have low correlations among the main effects, quadratic effects and two-factor...

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n,...

Theoretical results are derived for finding D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions. The upper bounds of the determinant of the related matrix for D-optimality are obtained. For run sizes 12 and 20, D-optimal orthogonal arrays...