Existence and construction of randomization defining contrast subspaces for regular factorial designs

Ranjan, Pritam; Bingham, Derek; Dean, Angela

doi:10.1214/08-aos644

Cited by 12 publications

(33 citation statements)

References 37 publications

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“…All the γ 2u 1 interactions form a saturated factorial design OA(p 2u 1 , p γ 2u 1 , 2). From the related results of Ranjan et al [12], we can easily have the following property for the N -cycle matrix.…”

Section: Construction Of Oas With Higher Hidden Strengthmentioning

confidence: 97%

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A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

2011

Front. Math. China

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Latin hypercube design is a good choice for computer experiments. In this paper, we construct a new class of Latin hypercube designs with some high-dimensional hidden projective uniformity. The construction is based on a new class of orthogonal arrays of strength two which contain higher strength orthogonal arrays after their levels are collapsed. As a result, the obtained Latin hypercube designs achieve higher-dimensional uniformity when projected onto the columns corresponding to higher strength orthogonal arrays, as well as twodimensional projective uniformity. Simulation study shows that the constructed Latin hypercube designs are significantly superior to the currently used designs in terms of the times of correctly identifying the significant effects.

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Section: Construction Of Oas With Higher Hidden Strengthmentioning

confidence: 97%

“…Here, we first introduce the so-called N -cycle scheme proposed by Ranjan et al [12]. It can be used to partition the effect space of a regular fractional factorial design.…”

Section: Construction Of Oas With Higher Hidden Strengthmentioning

confidence: 99%

A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

2011

Front. Math. China

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“…A set S of all non-null pencils formed by linear combinations of t independent randomization restriction factors in P constitutes a (t − 1)-dimensional For efficient analysis of multistage factorial experiments, it is desirable to construct disjoint RDCSSs. Ranjan et al (2009) established the existence of a set of disjoint RDCSSs in a 2 p factorial experiment via the existence of a spread of a P G(p − 1, 2).…”

Section: Rdcsss and Projective Geometriesmentioning

confidence: 99%

Space-filling Latin hypercube designs based on randomization restrictions in factorial experiments

Ranjan

Spencer

2014

Statistics & Probability Letters

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a b s t r a c tLatin hypercube designs (LHDs) with space-filling properties are widely used for emulating computer simulators. Over the last three decades, a wide spectrum of LHDs have been proposed with space-filling criteria like minimum correlation among factors, maximin interpoint distance, and orthogonality among the factors via orthogonal arrays (OAs). Projective geometric structures like spreads, covers and stars of PG(p − 1, q) can be used to characterize the randomization restriction of multistage factorial experiments. These geometric structures can also be used for constructing OAs and nearly OAs (NOAs). In this paper, we present a new class of space-filling LHDs based on NOAs derived from stars of PG(p − 1, 2).

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“…[4,9,11,13,15,19,20]. They can be used to construct error-correcting codes [6,8], orthogonal arrays [7,10], and recently factorial designs [22]. We let τ q (n, t) denote the minimum number of subspaces in any maximal partial tspread of V (n, q).…”

Section: Application To Maximal Partial T-spreadsmentioning

confidence: 99%

Extremal sizes of subspace partitions

Heden

Lehmann

Nastase

et al. 2011

Des. Codes Cryptogr.

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A subspace partition of V = V (n, q) is a collection of subspaces of V such that each 1-dimensional subspace of V is in exactly one subspace of . The size of is the number of its subspaces. Let σ q (n, t) denote the minimum size of a subspace partition of V in which the largest subspace has dimension t, and let ρ q (n, t) denote the maximum size of a subspace partition of V in which the smallest subspace has dimension t. In this article, we determine the values of σ q (n, t) and ρ q (n, t) for all positive integers n and t. Furthermore, we prove that if n ≥ 2t, then the minimum size of a maximal partial t-spread in V (n + t − 1, q) is σ q (n, t).

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Existence and construction of randomization defining contrast subspaces for regular factorial designs

Cited by 12 publications

References 37 publications

A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

Space-filling Latin hypercube designs based on randomization restrictions in factorial experiments

Extremal sizes of subspace partitions

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