Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Research and Training School (RTS)


Roy, Jogabrata (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

The advantages sample surveys over complete censuses are well known and seem to be fully appreaciated as is evidenced by the increasing use of sample surveys now a days as a means of collecting information.The use of probability theory to make rigorous inductive inferences has been well recognised for a long time. Such inferences can be made only when observations which form the basis of the infe- rence are generated by some chance mechanism, In traditional applica- tions, the statistician usually assume s or takes for granted some kind of chan ce mechanism behind the o bservations, where as in sample surveys or planned experiments the statistician consciously introduces the chance element by having recourse to the me chanism of randomisation, introduced by R.A.Fisher Z B5 /. Thủs has the advantage that the validity of the inferences does not depend on any extraneous assumptions. He demonstrated that a deliberately introduced randomisation in the selection of a part from the whole itself provides a valid method of obtaining a rigorous expression to the amount of error committed while arguing from a part to the whole.Another important concept introduced by P. C. Mahalanobis 24a 7 in this field, is the cost function. While the efficiency of a sample survey as measured by the precision of the estimate is important, it has to delicately balanced against the cost of the survey to 2 have a meaningful application of these techni ques in practice.The earlier developements in sampling theory of finite popula- tions relate ma in ly to a number of techniques of sampling appropriate to varians situations in practice, to estimate the total of real valued character defined for units of the population (briefly referred to as popula tion total. Significant advances in this direction are strati- fied sampling first studied by Neyman 29 7, multi stage sampling and use of auxiliary information first studied by Hanson and Hurnitz Z 20a 7, various me thods in current practice of using auxiliary infor- mation, are the ratio and regression me thods of estimation and proba bility proporti onal to size sampling, While for the first two methods it is not ne cessary to have the auxiliary information completely beforehand (and can even be collected al ong with the main information) but only its total for the entire popul ation, for the latter, it is ne cessary. However, the first two methods do not heve an exact small sample theory while for the last we have an exact theory.The earlier developments have been guided usually on heuristic considerations and attention limited to get at some unbiased estimators. It is only recently that a systematic investigation of sampling from finite populations has begun with the works of Hervitz and Thompson [22] and Godambe [11].The main contributions in this thesis relate to (1) a search for reasonable criteria of optimality and sampling strategies that one optimum under these criteria; (2) development of a unified opera- tional method drawing samples when a sampling design is partly or fully specified and (3) optimum utilisation of auxiliary information of a type commonly met with in practice.


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