Date of Submission

9-22-1982

Date of Award

9-22-1983

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Mukhopadhyay, Anis Chandra (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

The study of optimality of block designs formally began with wald (1943) proving a very important optimality property, designated as D-optimality of Iatin Square. Desi gns in a given physical set up. Next Ehrenfield (1955) proved the E-optimality property of Latin Square Designs. Since then, the work in: the area has primarily consisted in evolving a number of useful opti- mality oriteria for oomparing block design in a reasonable set up given and oharacterizing and/or constructing desi gns saiisfying the so called optimality criteria developed. But it was not until 1958, when the theory was given a proper and precise formu- lation with the probleme defined in a syst ematic and standardized manner by Kiefer. Restricting to the class of connected block designs, Kief er (1958, 1959) considered the general problem of est im at ion of a set of orthonormal treatment contrasts n = PT %3! and gave precise definitions of a number of standard optimality criteria including A, D- and E-optimality, for measuring the performances of the least square estimates of these treatment contrasts from the design. Given the parameters b= number of blocks, k constant block size and v = number of treatments, a BI ED, when it exists , was proved to be optimal with regard to all Felevant optimality criteria defined by Kiefer (1956). the same time Mote (1958) proved the E-optimality and Khirsagar (1958) the A- and D-optimality of the BI BDs independently in the same set up.Roy (1958) took up the problem of estimation of - 2 - all elementary treatment contrasts and proved that the most efficient design for this problem for given b,k and withefficient design for this problem for glven b,k and with regard to A-optimality criterian is a BIBD, when it exists Kiefer (1975) defined a very general class of optimality critoria including the previously considered and widely used A-, D and E-optimality criteria. He also generalised the BIBDs to define BBDs (which reduced to the former in the special case k< v) and proved their universal optimality property, i.c. their optimal property with regard to every optimality criterion belonging to the general class defined by him. The major part o this paper was devoted to the optimality st udy of designs in a two-way heterogeneity setting, which we discuss in a laite paragraph.First result on the optimality of asymmetrical designs was established by Takeuchi (1961). Using a new technique, le proved the B-optimality of the GDDs with λ2=λ1+1 Laler, Contrfe and Stone (1974) derived an improved upper bound to the efficien of a block design with regard to A-optimality criterion. Cheng (1978b) sed a technique similar to that used by Conniffe and Stone (1974) to establish the optimality of the MBGDDs of typo 1.e. the DDs with m = 2 andλ2=λ1+1 with regard to a general class of optimality criteria termed by him t- optimali criteria of type 1, which included the age old A-, D and E-optimality criteria montioned before.

Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842825

Control Number

ISILib-TH74

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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