Theory of Optimal Designs

ISBN-13: 9780387969916 / Angielski / Miękka / 1989 / 171 str.

Kirti R. Shah; Bikas K. Sinha

Opis

There has been an enormous growth in recent years in the literature on discrete optimal designs. The optimality problems have been formulated in various models arising in the experimental designs and substantial progress has been made towards solving some of these. The subject has now reached a stage of completeness which calls for a self-contained monograph on this topic. The aim of this monograph is to present the state of the art and to focus on more recent advances in this rapidly developing area. We start with a discussion of statistical optimality criteria in Chapter One. Chapters Two and Three deal with optimal block designs. Row-column designs are dealt with in Chapter Four. In Chapter Five we deal with optimal designs with mixed effects models. Repeated measurement designs are considered in Chapter Six. Chapter Seven deals with some special situations and Weighing designs are dis cussed in Chapter Eight. We have endeavoured to include all the major developments that have taken place in the last three decades. The book should be of use to research workers in several areas including combinatorics as well as to the experimenters in diverse fields of applications. Since the details of the construction of the designs are available in excellent books, we have only pointed out the designs which have optimality proper ties. We believe, this will be adequate for the experimenters."

Spis treści

1. Optimality Criteria In Design of Experiments.- 1. General Objectives.- 2. The Linear Model Set-up.- 3. Choice of Optimality Criteria.- References.- 2. Block Designs: General Optimality.- 1. Introduction.- 2. Universal Optimality of the BBDs.- 3. Optimality of Some Classes of Asymmetrical Designs w.r.t the Generalized Criteria.- References.- 3. Block Designs: Specific Optimality.- 1. Introduction.- 2. E-optimal Designs.- 3. Efficiency Factor and A-optimal Designs.- 4. MV-optimal Designs.- 5. D-optimal Designs.- 6. Regular Graph Designs and John-Mitchell Conjecture.- 7. Optimal Designs with Unequal Block Sizes.- References.- 4 Row-Column Designs.- 1. Introduction.- 2. Universal Optimality of the Regular GYDs.- 3. Nonregular GYDs: Specific Optimality Results.- 4. Optimality of Other Row-Column Designs.- References.- 5. Mixed Effects Models.- 1. Introduction.- 2. Optimality Aspects of Block Designs Under a Mixed Effects Model.- 3. Optimality of GYDs Under a Mixed Effects Model.- 4. Concluding Remarks.- References.- 6. Repeated Measurements Designs.- 1. Introduction.- 2. The Linear Model(s), Definitions and Notations.- 3. Universal Optimality of Strongly Balanced Uniform RMDs.- 4. Universal Optimality of Nearly Strongly Balanced Uniform RMDs.- 5. Universal Optimality of Balanced Uniform RMDs.- 6. Concluding Remarks.- References.- 7. Optimal Designs For Some Special Cases.- 1. Introduction.- 2. Models with Correlated Observations.- 3. Models with Covariates.- 4. Designs for Comparing Treatments vs. Control.- References.- 8. Weighing Designs.- 1. Introduction.- 2. A Study of Chemical Balance Weighing Designs.- 3. A Study of Spring Balance Weighing Designs.- 4. Optimal Estimation of Total Weight.- 5. Miscellaneous Topics in Weighing Designs.- References.- Author Index.