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)


Rao, J. J.

Abstract (Summary of the Work)

The main problam of sampling from finite populations consi sts of devi sing an appropriate proceduro for sel ecting a sample from a given population and developing an appropriate procedure for estimating the population parameter of interest in order to maximize the precision of the estimator subject to certain restrictions on the cost for the survey or alternatively minimi ze the cost for achieving a given l evel of precision. During the thirties and forties several contributions were made to develop the theoretical background of sample survey techni ques in order to solve this problem, The most significant works of Cochran, Hansen, Hurwitz, Mahalanobis, Neyman, Sukhatme and Yates among others may be mentioned in this context. As well as developing the theoretical techni ques, practical techni ques for the actual conduct of a survey, data collection and analysis were oonsidered which rosulted in largo scalo sample surveys (Mahalanobis (1944), (1946)).In most of the sample survey situations information on an aux111ary variate closely related to the study variato is available, Efficient uti11 sation of this auxiliary information for selection purposes and for estimation gave rise to the varying probability selcction,method and tho thoory of ratio and egression estimators and stratification tochnique (See Nayman (1934), Cochran (1942) and Hansen and Hurwltz (1943)). For reviews on the devolopments in the thoo ry of sampling from finite populations we rofer to Yates (1946), Cochran (1947), st ephen (1948), Seng (1951), Sukhatme( (1959),(1966)), Dalenius (1962), Murthy (1963), Vos (1974) and more recently Smith (1976a). Horvitz and Thompson (1952) formulat ed a syst amatic thoory of sempling from finite populations and defined three classos of estimators, Later in 1955, Godam be proposod a unified theory of sempling fron finite populations with a viow to discussing the fundamental problems of sempling within this framework. Codambe (1955) established that for any semple design there doos not exd st a uniformly minimm variance unbiased estimator of the population total in the class of linear unbiased estimators (barring certain exceptions, charact ori zod lator by Hamurav (1965)). Since than various criteria such as admissibility, 1inear-invariance,regularity, hyperadmissi bility! among others have been putforward for the choico of an optimum ostimator, Whenever we have auxdliary information on a character- 1stic closely related to the study variable it was first shown by Cochran (1946) that this information can be utili sed to sot up a criterion of optimality of minimum expectod variance under suitably defined model. This concept is popularly referred as the super population concept. In this thesis we work th the general supor population model denotod by e(g), 20 while discussing the choice of an optimum strategy for itimating the population total (see chapters 5 and 6). Under stratified set up, when the sup er population model e(g) 1s tephrased to apply in a stratifiod situation, in chapters 2,3 and 7 ve discus the choice between unstratifiod sempling strategy and stratified strategies with various allocations of Semple size to strata.We give balow a brief sturimary of the authors contributions containod in this thesis.Following the introductory chapter 0, we give in chapter 1 the basic definitions and explain the concepts that are used in the sequel.


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