43,125 research outputs found
Optimal designs for mixed models in experiments based on ordered units
We consider experiments for comparing treatments using units that are ordered
linearly over time or space within blocks. In addition to the block effect, we
assume that a trend effect influences the response. The latter is modeled as a
smooth component plus a random term that captures departures from the smooth
trend. The model is flexible enough to cover a variety of situations; for
instance, most of the effects may be either random or fixed. The information
matrix for a design will be a function of several variance parameters. While
data will shed light on the values of these parameters, at the design stage,
they are unlikely to be known, so we suggest a maximin approach, in which a
minimal information matrix is maximized. We derive maximin universally optimal
designs and study their robustness. These designs are based on semibalanced
arrays. Special cases correspond to results available in the literature.Comment: Published in at http://dx.doi.org/10.1214/07-AOS518 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Efficient Two-Stage Group Testing Algorithms for Genetic Screening
Efficient two-stage group testing algorithms that are particularly suited for
rapid and less-expensive DNA library screening and other large scale biological
group testing efforts are investigated in this paper. The main focus is on
novel combinatorial constructions in order to minimize the number of individual
tests at the second stage of a two-stage disjunctive testing procedure.
Building on recent work by Levenshtein (2003) and Tonchev (2008), several new
infinite classes of such combinatorial designs are presented.Comment: 14 pages; to appear in "Algorithmica". Part of this work has been
presented at the ICALP 2011 Group Testing Workshop; arXiv:1106.368
Some results on designs of resolution IV with (weak) minimum aberration
It is known that all resolution IV regular designs of run size
where must be projections of the maximal even design
with factors and, therefore, are even designs. This paper derives a
general and explicit relationship between the wordlength pattern of any even
design and that of its complement in the maximal even design. Using
these identities, we identify some (weak) minimum aberration designs
of resolution IV and the structures of their complementary designs. Based on
these results, several families of minimum aberration designs of
resolution IV are constructed.Comment: Published in at http://dx.doi.org/10.1214/08-AOS670 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Frame difference families and resolvable balanced incomplete block designs
Frame difference families, which can be obtained via a careful use of
cyclotomic conditions attached to strong difference families, play an important
role in direct constructions for resolvable balanced incomplete block designs.
We establish asymptotic existences for several classes of frame difference
families. As corollaries new infinite families of 1-rotational
-RBIBDs over are
derived, and the existence of -RBIBDs is discussed. We construct
-RBIBDs for , whose
existence were previously in doubt. As applications, we establish asymptotic
existences for an infinite family of optimal constant composition codes and an
infinite family of strictly optimal frequency hopping sequences.Comment: arXiv admin note: text overlap with arXiv:1702.0750
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