Robustness and Optimality in Experiment Design

Organizer: Boxin Tang, Simon Fraser University
Session Chair: David J. Edwards, Virginia Commonwealth University


Construction of Low Aberration Strength-Two Orthogonal Arrays

Robert Mee and Xin Lu
University of Tennessee - Knoxville

Complementary design results are very helpful for constructing resolution III fractional factorial designs with minimum aberration. While the same guarantees of minimum (G2) aberration do not hold for constructing strength-two nonregular designs, complementary design ideas may still provide some utility in constructing good orthogonal arrays. We explore this and other methods for identifying good strength-two orthogonal arrays where the design is not saturated and where complete enumeration of orthogonal arrays has not yet been achieved.


Robustness of Design in Dose-Response Studies

Doug Wiens
University of Alberta

In work carried out with my colleague Pengfei Li, we construct experimental designs for dose-response studies. The designs are robust against possibly misspecified link functions; to this end they minimize the maximum mean squared error of the estimated dose required to attain a response in 100p% of the target population. Here p might be one particular value - p=0.5 that corresponds to ED50 estimation - or it might range over an interval of values of interest. The maximum of the mean squared error is evaluated over a Kolmogorov neighbourhood of the fitted link. Both the maximum and minimum must be evaluated numerically; the former is carried out by quadratic programming and the latter by simulated annealing.


Optimal Supersaturated Design for Variable Selection via Lasso

Yu Michael Zhu
Purdue University

Supersaturated design is a type of design that has more columns than rows and is typically used for screening experiments in which the number of factors exceeds the number of runs. In the literature, various criteria have been proposed for constructing optimal supersaturated designs. Most existing criteria are motivated and further justified from the estimation perspective. However, when an experiment employs a supersaturated design, its usual objective is to screen important factors from a large pool of factors, which is essentially variable selection. Lately, as a new variable selection method, Lasso has received much attention, mainly due to its capability to select variables even when there are less observations. In this talk, we will propose a number of optimality criteria for the construction of supersaturated design from the perspective of variable selection with Lasso. The properties of these criteria will be discussed. A computing algorithm will be used to construct such optimal supersaturated designs, and examples of simulation and real applications will also be presented. This is joint work with Hong Wan and Dadi Xing at Purdue University