Minimum breakdown designs in blocks of size two
01 Jan 2013-Journal of Statistical Planning and Inference (North-Holland)-Vol. 143, Iss: 1, pp 202-208
TL;DR: In this paper, the minimum breakdown criterion is proposed to quantify the robustness of designs in blocks of size two and a new class of robust designs, called minimum breakdown designs, is defined.
About: This article is published in Journal of Statistical Planning and Inference.The article was published on 2013-01-01. It has received 10 citations till now. The article focuses on the topics: Block design & Robustness (computer science).
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Journal Article•
TL;DR: In this article, two simple pilot procedures are proposed for avoiding the problem of dealing with a disconnected experimental design, which are carried out on the selected design before any experimentation is considered.
Abstract: Summary. Two simple pilot procedures are proposed for avoiding the problem of dealing with a disconnected experimental design. Both procedures should be carried out on the selected design before any experimentation is considered. The first procedure is a check that the suggested design is connected with respect to treatments. This makes use of the information matrix for the model and provides feed-back on a disconnected design. The second procedure specifies which observations are influential in causing a connected design to become disconnected, with respect to any set of parameter effects, if these observations are lost during the experimental period. This specification is found by examining the projection matrix for the model. These pilot procedures are illustrated by several examples.
26 citations
TL;DR: In this paper, the robustness of resolvable incomplete block designs in the event of two patterns of missing observations (loss of whole blocks and loss of whole replicates) was investigated.
7 citations
TL;DR: In this article, conditions for connectivity and robustness of row column designs with blocks of size two were obtained using combinatorial arguments and results from graph theory, and lower bounds for the breakdown number in terms of design parameters were given.
Abstract: Designs with blocks of size two have numerous applications. In
experimental situations where observation loss is common, it is im-
portant for a design to be robust against breakdown. For designs
with one treatment factor and a single blocking factor, with blocks
of size two, conditions for connectivity and robustness are obtained
using combinatorial arguments and results from graph theory. Lower
bounds are given for the breakdown number in terms of design pa-
rameters. For designs with equal or near equal treatment replication,
the concepts of treatment and block partitions, and of linking blocks,
are used to obtain information on the number of blocks required to
guarantee various levels of robustness. The results provide guidance
for construction of designs with good robustness properties.
Robustness conditions are also established for row column designs
in which one of the blocking factors involves blocks of size two. Such
designs are particularly relevant for microarray experiments, where
the high risk of observation loss makes robustness important. Dis-
connectivity in row column designs can be classified as three types.
Techniques are given to assess design robustness according to each
type, leading to lower bounds for the breakdown number. Guidance
is given for robust design construction.
Cyclic designs and interwoven loop designs are shown to have good
robustness properties.
6 citations
TL;DR: In this article, the robustness of a binary block design against the loss of whole blocks is evaluated based on summing entries of selected upper non-principal sections of the concurrence matrix.
Abstract: © 2015 Australian Statistical Publishing Association Inc. Criteria are proposed for assessing the robustness of a binary block design against the loss of whole blocks, based on summing entries of selected upper non-principal sections of the concurrence matrix. These criteria improve on the minimal concurrence concept that has been used previously and provide new conditions for measuring the robustness status of a design. The robustness properties of two-associate partially balanced designs are considered and it is shown that two categories of group divisible designs are maximally robust. These results expand a classic result in the literature, obtained by Ghosh, which established maximal robustness for the class of balanced block designs.
5 citations
Journal Article•
TL;DR: This paper identifies designs for k ≤ 8 factors that enable estimation of all main effects and two-factor interactions with the fewest number of replications and gives a construction for general k that gives more economical designs than previously published.
Abstract: [This abstract is based on the author's abstract.]When the experimental goal is to estimate both main effects and two-factor interactions in two-level designs run in blocks of two sizes, it is necessary to combine replicates of the experiment that use d..
3 citations
References
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14 Nov 1995
TL;DR: In this article, the authors introduce the concept of graph coloring and propose a graph coloring algorithm based on the Eulers formula for k-chromatic graphs, which can be seen as a special case of the graph coloring problem.
Abstract: 1. Fundamental Concepts. Definitions and examples. Paths and proofs. Vertex degrees and counting. Degrees and algorithmic proof. 2. Trees and Distance. Basic properties. Spanning trees and enumeration. Optimization and trees. Eulerian graphs and digraphs. 3. Matchings and Factors. Matchings in bipartite graphs. Applications and algorithms. Matchings in general graphs. 4. Connectivity and Paths. Cuts and connectivity. k-connected graphs. Network flow problems. 5. Graph Coloring. Vertex colorings and upper bounds. Structure of k-chromatic graphs. Enumerative aspects. 6. Edges and Cycles. Line graphs and edge-coloring. Hamiltonian cycles. Complexity. 7. Planar Graphs. Embeddings and Eulers formula. Characterization of planar graphs. Parameters of planarity. 8. Additional Topics. Perfect graphs. Matroids. Ramsey theory. More extremal problems. Random graphs. Eigenvalues of graphs. Glossary of Terms. Glossary of Notation. References. Author Index. Subject Index.
7,126 citations
TL;DR: It is shown that KNNimpute appears to provide a more robust and sensitive method for missing value estimation than SVDimpute, and both SVD Impute and KNN Impute surpass the commonly used row average method (as well as filling missing values with zeros).
Abstract: Motivation: Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and K-means clustering are not robust to missing data, and may lose effectiveness even with a few missing values. Methods for imputing missing data are needed, therefore, to minimize the effect of incomplete data sets on analyses, and to increase the range of data sets to which these algorithms can be applied. In this report, we investigate automated methods for estimating missing data. Results: We present a comparative study of several methods for the estimation of missing values in gene microarray data. We implemented and evaluated three methods: a Singular Value Decomposition (SVD) based method (SVDimpute), weighted K-nearest neighbors (KNNimpute), and row average. We evaluated the methods using a variety of parameter settings and over different real data sets, and assessed the robustness of the imputation methods to the amount of missing data over the range of 1–20% missing values. We show that KNNimpute appears to provide a more robust and sensitive method for missing value estimation than SVDimpute, and both SVDimpute and KNNimpute surpass the commonly used row average method (as well as filling missing values with zeros). We report results of the comparative experiments and provide recommendations and tools for accurate estimation of missing microarray data under a variety of conditions. Availability: The software is available at http://smi-web.
3,542 citations
TL;DR: In this paper, the authors examined experimental design issues arising with gene expression microarray technology and provided a general set of recommendations for design with microarrays, illustrated in detail for one kind of experimental objective, where they also gave the results of a computer search for good designs.
Abstract: We examine experimental design issues arising with gene expression microarray technology. Microarray experiments have multiple sources of variation, and experimental plans should ensure that eects of interest are not confounded with ancillary eects. A commonly-used design is shown to violate this principle and to be generally inecient. We explore the connection between microarray designs and classical block design and use a family of ANOVA models as a guide to choosing a design. We combine principles of good design and A-optimality to give a general set of recommendations for design with microarrays. These recommendations are illustrated in detail for one kind of experimental objective, where we also give the results of a computer search for good designs.
701 citations
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
420 citations