DD-optimal saturated designs: a simulation study

In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric structure of the design and we compare them with the classical $D$-efficiency criterion. We perform a simulation study. In all the test cases we observe that designs with high values of $D$-efficiency have also high values of the new objective functions.Comment: 8 pages. Preliminary version submitted to the 7th IWS Proceeding

Model-Oriented Data Analysis; Proceedings of the 3rd International Workshop in Petrodvorets, Russia, May 25-30 1992

This volume contains the majority of papers presented at the Third Model-Oriented Data Analysis Workshop/Conference (MODA3) in Petrodvorets, Russia on 25-30 May 1992. As with the previous two workshops in 1987 and 1990, the conference covers theoretical and applied statistics with a heavy emphasis on experimental design. Under these broad headings other specialised topics can be mentioned, particularly quality improvements and optimization. This proceedings volume consists of three main parts: I. Optimal Design, II. Statistical Applications, III. Stochastic Optimization. A constant theme at MODA conferences is the subject of optimal experimental design. This was well represented at MODA3 and readers will find important contributions. In recent years the model investigated under this heading have become progressively more complex and adaptive

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

G-majorization with applications to matrix orderings

AbstractA vector x is said to G-majorize a vector y if y lies in the convex hull of the orbit of x under a group G. The present paper contains a straightforward account with two important statements equivalent to G-majorization. In certain cases, for example when G is a finite reflection group, one equivalent condition reduces to a finite set of linear inequalities representing a cone ordering in the fundamental region of the group. The other condition is that every convex G-invariant function of y is less than the same function of x. Upper and lower weak majorizations (GW-majorizations) are introduced by combining G with a second ordering compatible with it. The results are applied where possible to matrix orderings where A≺GB is G-majorization when G is a subgroup of the orthogonal group On acting by congruence, i.e. g(B)=QBQT with Q the matrix representation for an element of On. When G is the symmetric group of permutation matrices this defines a new ordering and generalizes a proposition of Kiefer in the design of experiments

The ENBIS-11 Quality and Reliability Engineering International Special Issue

This is the editorial of the ENBIS-11 special issue