Date of Submission

7-28-1976

Date of Award

7-28-1977

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Ghosh, Jayanta Kumar (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

The study of admissible decision procedures began in late forties when Wald introduced the concept to characterize the minimal complete class of decision procedures. Starting with the pioneering work of Abraham Wald, there has been considerable contribution to this area over the last three decades. However, most of the articles in this field dealt with specific decision procedures arid studied their admissibility. It was Stein [11 who first characterized, admissible decision procedures. Farrell ([2], (3]) generalized the result of Stein. In spite of the works of Stein and Farrell the problem of deciding whether a given decision procedure is admissible or not remained difficult even in smooth set ups. The reason for this is the necessary and sufficient conditions given by Stein-Farrells theorea are not easy to check.A major contribution towards this problem was made Brown [1J in 1971. In this brilliant article, he showed that the study of the admissibility of generalized Bayes estimators, under quadratic loss, of the mean of a multivaria te normal distribution could be linked up with a calculus of variation problem. By establishing a relation between the calculus of variation problem and the recurrence of a diffusion proceas, he characterized the admissible estimators under some conditions. This charecterization yields casily verifiable conditions. Apart from this, the link between admissibility and the recurrence of the associated diffusion process is interesting and novel. In this dissertation we extend the results of Brown [11. We give a chapterwise surmary below.In Chapter I we deal with exterior boundary value probla and relate them to a calculus of variation problem. These exterior boundary value problems play crucial in the rest o this dissertation.The main regults of Chapter II are generalizations of Browms results (Brown [1]). Turther, our proofs differ fro his. While he goes through diffusion processes, we resort to exterior boundary value problens. Our method gives a shorter proof of the main theorem of Brom [1]. Chapter III is devoted to, the admissible estimators of Browns results(Brown [1].

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:28842975

Control Number

ISILib-TH35

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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