Block Designs: Analysis, Combinatorics and Applications by Damaraju Raghavarao, Lakshmi V Padgett | | 9789812563606 | Hardcover | Barnes & Noble
Block Designs: Analysis, Combinatorics and Applications

Block Designs: Analysis, Combinatorics and Applications

by Damaraju Raghavarao, Lakshmi V Padgett
     
 

ISBN-10: 9812563601

ISBN-13: 9789812563606

Pub. Date: 11/10/2005

Publisher: World Scientific Publishing Company, Incorporated

Combinatorial mathematicians and statisticians have made a wide range of contributions to the development of block designs, and this book brings together much of that work. The designs developed for a specific problem are used in a variety of different settings. Applications include controlled sampling, randomized response, validation and valuation studies,

Overview

Combinatorial mathematicians and statisticians have made a wide range of contributions to the development of block designs, and this book brings together much of that work. The designs developed for a specific problem are used in a variety of different settings. Applications include controlled sampling, randomized response, validation and valuation studies, intercropping experiments, brand cross-effect designs, lotto and tournaments.The intra- and inter- block, nonparametric and covariance analysis are discussed for general block designs, and the concepts of connectedness, orthogonality, and all types of balances in designs are carefully summarized. Readers are also introduced to the designs currently playing a prominent role in the field: alpha designs, trend-free designs, balanced treatment-control designs, nearest neighbor designs, and nested designs.This book provides the important background results required by researchers in block designs and related areas and prepares them for more complex research on the subject.

Product Details

ISBN-13:
9789812563606
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
11/10/2005
Series:
Series on Applied Mathematics
Edition description:
New Edition
Pages:
224
Product dimensions:
6.10(w) x 9.00(h) x 0.80(d)

Table of Contents

Prefacexi
1Linear Estimation and Tests for Linear Hypotheses1
1.1The Model1
1.2Estimability and Best Linear Unbiased Estimators2
1.3Least Squares Estimates6
1.4Error Functions7
1.5Weighted Normal Equations9
1.6Distributions of Quadratic Forms9
1.7Tests of Linear Hypotheses13
2General Analysis of Block Designs16
2.1Preliminaries16
2.2Intrablock Analysis of Connected Designs17
2.3A Numerical Example23
2.4Analysis of Incomplete Block Designs with Recovery of Interblock Information24
2.5Nonparametric Analysis26
2.6Orthogonality28
2.7Variance and Combinatorial Balance30
2.8Efficiency Balance35
2.9Calinski Patterns37
2.10Optimality38
2.11Transformations40
2.12Covariance Analysis42
3Randomized Block Designs45
3.1Analysis with Fixed Block Effects45
3.2Analysis with Random Block Effects49
3.3Unequal Error Variances50
3.4Permutation Test51
3.5Treatment Block Interactions51
4Balanced Incomplete Block Designs - Analysis and Combinatorics54
4.1Definitions and Basic Results54
4.2Intra- and Inter-Block Analysis56
4.3Set Structures and Parametric Relations58
4.4Related Designs65
4.5Construction of BIB Designs from Finite Geometries71
4.6Construction by the Method of Differences72
4.7A Statistical Model to Distinguish Designs with Different Supports77
4.8Non-Existence Results77
4.9Concluding Remarks79
5Balanced Incomplete Block Designs - Applications86
5.1Finite Sample Support and Controlled Sampling86
5.2Randomized Response Procedure87
5.3Balanced Incomplete Cross Validation90
5.4Group Testing90
5.5Fractional Plans to Estimate Main Effects and Two-Factor Interactions Inclusive of a Specific Factor93
5.6Box-Behnken Designs94
5.7Intercropping Experiments96
5.8Valuation Studies98
5.9Tournament and Lotto Designs104
5.10Balanced Half-Samples106
6t-Designs108
6.1Introduction108
6.2Inequalities on b109
6.3Resistance of Variance Balance for the Loss of a Treatment110
6.4Constructions111
6.5A Cross-Effects Model114
7Linked Block Designs117
7.1Dual Designs - Linked Block Designs117
7.2Intra-Block Analysis119
7.3Optimality119
7.4Application of LB Designs in Successive Sampling121
8Partially Balanced Incomplete Block Designs124
8.1Definitions and Preliminaries124
8.2Some Known Association Schemes127
8.3Intra-Block Analysis135
8.4Some Combinatorics and Constructions139
8.5Partial Geometric Designs146
8.6Applications to Group Testing Experiments147
8.7Applications in Sampling151
8.8Applications in Intercropping151
8.9Concluding Remarks153
9Lattice Designs155
9.1Introduction155
9.2Square Lattice Designs156
9.3Simple Triple Lattice159
9.4Rectangular Lattice159
10Miscellaneous Designs162
10.1[alpha]-Designs162
10.2Trend-Free Designs164
10.3Balanced Treatment Incomplete Block Designs165
10.4Nested Block Designs167
10.5Nearest Neighbor Designs169
10.6Augmented Block Designs170
10.7Computer Aided Block Designs171
10.8Design for Identifying Differentially Expressed Genes172
10.9Symmetrical Factorial Experiments with Correlated Observations in Blocks175
References and Selected Bibliography179
Author Index203
Subject Index207

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