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The stochastic search variable selection proposed by George and McCulloch (J Am Stat Assoc 88:881–889, 1993) is one of the most popular variable selection methods for linear regression models. Many efforts have been proposed in the literature to improve its computational efficiency. However, most of these efforts change its original Bayesian formulation, thus the comparisons are not fair. This work...
The Latin hypercube design (LHD) is a popular choice of experimental design when computer simulation is used to study a physical process. In this paper, we propose some methods for constructing nearly orthogonal Latin hypercube designs (NOLHDs) with 2, 4, 8, 12, 16, 20 and 24 factors having flexible run sizes. These designs can be very useful when orthogonal Latin hypercube designs (OLHDs) of the...
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 interactions. On the other hand, OLHDs are hard to be found due to their large number of levels for each factor....
Supersaturated designs (SSDs) have been highly valued in recent years for their ability of screening out important factors in the early stages of experiments. Recently, Liu and Lin (in Statist Sinica 19:197–211, 2009) proposed a method to construct optimal mixed-level SSDs from smaller multi-level SSDs and transposed orthogonal arrays (OAs). This paper extends their method to construct more equidistant...
Various optimal criteria have been proposed to rank asymmetrical fractional factorial designs. Among them, the generalized minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention. Recently, Liu et al. (Stat Sin 16:1285–1297, 2006) proposed the minimum χ2 criterion in terms of level-combinations. In this paper, the equivalency of the...
Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the...
The asymmetrical or mixed-level factorial design is a kind of important design in practice. There is a natural problem on how to choose an optimal (s2)sn design for the practical need, where s is any prime or prime power. This paper considers the clear effects criterion for selecting good designs. It answers the questions of when an (s2)sn design with fixed number of runs contains clear two-factor...
The discrepancy is an important optimality criterion for experimental designs. Sometimes for practical reasons one may choose a design on some finite subset of the original experimental domain. This article addresses the question of whether minimum discrepancy designs are the same for the discrepancy defined on the original experimental domain and the discrepancy defined on a subset. Under certain...
. Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking factor. In this paper, the definition of combined-optimal design is extended to the case when blocking factor is significant, and this new...
Abstract. Supersaturated designs have become increasingly popular in recent years because of their potential in saving run size and the technical novelty. In this paper, the minimum generalized aberration (MGA) criterion proposed by Ma and Fang (2001) (and another two equivalent criteria proposed by Xu and Wu (2001) and Xu (2001b) respectively) for comparing non-regular symmetrical designs is used...
A supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. In this paper, E(fNOD) criterion is employed for comparing supersaturated designs from the viewpoint of orthogonality and uniformity, and a lower bound of E(fNOD) which can serve as a benchmark of design optimality is obtained. It is shown that the existing E(s2)...
Supersaturated designs have become increasingly popular in recent years because of their potential in saving run size and the technical novelty. In this paper, the minimum generalized aberration (MGA) criterion proposed by Ma and Fang (2001) (and another two equivalent criteria proposed by Xu and Wu (2001) and Xu (2001b) respectively) for comparing non-regular symmetrical designs is used for evaluating...
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