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For designs of computer experiments, two important and desirable properties are projection uniformity and column-orthogonality. However, it is always a challenging task to construct designs with both properties. This paper constructs a series of designs which possess both (near) column-orthogonality and projection uniformity, called (nearly) column-orthogonal mappable nearly orthogonal arrays (MNOAs). Furthermore, we enhance the MNOAs’ projection uniformity on any one dimension by using the constructed (nearly) column-orthogonal MNOAs and rotation matrices. Compared with the existing results (such as Sun and Tang in J Am Stat Assoc 112:683–689, 2017), the newly constructed designs are able to accommodate more design columns and have a much better projection uniformity, for the same run sizes.

Space-filling designs are widely used in computer experiments. They are frequently evaluated by the orthogonality and distance-related criteria. Rotating orthogonal arrays is an appealing approach to constructing orthogonal space-filling designs. An important issue that has been rarely addressed in the literature is the design selection for the initial orthogonal arrays. This paper studies the maximin L2-distance properties of orthogonal designs generated by rotating two-level orthogonal arrays under three criteria. We provide theoretical justifications for the rotation method from a maximin distance perspective and further propose to select initial orthogonal arrays by the minimum G2-aberration criterion. New infinite families of orthogonal or 3-orthogonal U-type designs, which also perform well under the maximin distance criterion, are obtained and tabulated. Examples are presented to show the effectiveness of the constructed designs for building statistical surrogate models.

We propose a new scalar and shift transform invariant test statistic for the high-dimensional two-sample location problem. Theoretical results and simulation studies show the good performance of our test under certain circumstances. [ABSTRACT FROM AUTHOR]

Abstract: Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.

Abstract: Discrepancy is an important criterion for uniformity in the design of experiments. Basically, it measures the distance between two functions: the empirical distribution of the design points and the theoretical uniform distribution function. This paper studies the properties of uniformity when the factor level values are contaminated with errors. Specifically, our study focuses on the wrap-around -discrepancy. It is shown that uniform designs with errors are less uniform (in the average sense) than the original ones without errors. Related theorems are obtained. Furthermore, it can be shown that the lattice sampling outperforms Latin hypercube sampling. The latter can be viewed as a lattice sampling with error-in-level values. [Copyright &y& Elsevier]

Screening is an important step of experimental design. It aims to identify a few active factors, among a large number of potential factors. In this paper, we propose two classes of mixed-level screening designs with desirable design properties; such as, low correlations between any two design columns, high design efficiencies (e.g., D- or A-efficiencies), and orthogonality between main effects and two-factor interactions. Conference matrices with skew-symmetric structure play an important role in the proposed construction. Two new construction methods for conference matrices with skew-symmetric structure, recursive and algebraic constructions, are provided. It is shown that the proposed mixed-level screening designs have all desirable design properties and do not require any computer search. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we derive a central limit theorem for marginally coupled designs that are intended for computer experiments with both qualitative and quantitative factors. This result is useful for establishing confidence intervals for estimators in various statistical applications. [ABSTRACT FROM AUTHOR]