Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Murthy, M. N.

Abstract (Summary of the Work)

Sample survny an a tochnique for collantion of data haa been w1dely accepted since quite a long time and it is only during the thirties and forties that a more syetem matic development has taken place owing to the most signi- ficant and rcmarkable works of Cochran, Hansen, Hurwitz, Mahalanobie, Neyman, Sukhatme, Yates and othera. Daring thin period, there were many important advances and tremendous progress in this field was achieved in India under the direction of Professor P. C. Mahal anobis. Besides the theoretical developments, streen was laid on the practical techniques and large-scale sample aurveys played a major rôle in thin context (Mahalanobia (1944), (1946 1).towarde the beginning of the second half of this period, Neyman (1934), Hansen and Hurwitz (1943) and Cochren (1942) considered the probleme of atratification and the question of utllisation of auxiliary inforsation for selectinn purposes and for estimation, which gave rise to the varying probabtlity eelection method and the theory of ratio and regreesion entimates. Madow and Madow (1944) developed the theory of syetenatic saunpling.Theae earller devolopments in sempling theory of finite populations, concerned with the techniquen of samp- 1ing, suited to the situations that aroee in practice and mainly dealt with the probleme of estimation of po pulation parametere auch an totale, meann or rati1on and their Roviewn of the devolopnents of theory of nampling from errore. finite populations wore publiehod by Yates (1946), stephan [1948), Beng (1951] and others. It wan Horvits and Thompe on in 1952 who first rocognized the nead for dealing ays tema- t1eally with the theory of sampling from finits populations and beeiden formulating the theory neatly, they defi ned three classes of estimators. Later 1n 1955, Godambe pro- posed a ifiod theory of eampling from finite popula tions, with a view to discuss tho fundamental problens of sampling within this framewor'k and also formulnted the definition of 2inearity wi th & general theory of nampling. Godambo [1955] han ostabllabed that for any aampla design there does not cxist a uniformly minimum variance unbiased estinetor of the population total in the clana of all linear unbiaevd cstimstors (rith aogo axceptions, charac- terised by Hanurar (1965] lntor). Shie leada to the chotce of ostinatorn trom the claan of adainaible entimators and varicue othor criteria have bean put fortard to arrive at an optimum choiee. Hunurav i1965, 1966) racontly introdu- ced the concept of hyper admiasibility and proved that the entinator due to Horvite and Thompi on (1952] is byper sdmissible. It was firet s ho wn hy Cochran (2946) that whenever we have auxiliary infornation on a charaoteriatic cloeely relatud to the study variable, wn aan utilise that infor- nation by considoring a stochạatic modul, shich he called 8n the auper-puptulation conoept, the idea being taken froe the Bayeninn inferenon. Godanbu (1955) hae proved that in the clane of all eampling strategion (sanpling design together with an eetimator being oalled a ntretogy (Hájek (1988])) with > d1stinet unite, strategy which has (1) the aane number of dintinet unita for every aasple, (11) the inclusinn probability of any unit t1# proportional to tha Ruxiliary information on that unit and (111) the eetimator in the corresponding Horvits-7hompson ostimater is the best in Bayusian sensa.


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