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, T. J. (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

The main problem of Survey sapling fron finite populations consista of devistng an appropriate procodure for solecting a rapresentative srple frøn a glven popalation and dornloping an apprepriate procedure for the estimation of the population parceeter of interest guch as po pulation nean or total or population ratto with a viev to naxinising the preofsion of the estinstor vithin the available resources of tino and ooat or 6iternati vely minimising the aost for achieving a giren level of prestsion, Towards the solution of this problen 1t is only during the thirties ond forties that a nore systematie develop- nant has taken place owing to the outstanding ard ploneering contributiona of Cochran, Hannen, Harvita, Mardow, Mahalanobds, Neyman, Bakhatmn, Yates and others, Thoretieal developments as well as practieal techniques wero considered and largo-satie agriezltural aud socio-oconoaia surveya played a sajar rôle in this context Mahal ane bis (144, 4c) aukhntmo (1945, 46) and Yatos (1947)),During the noxrt deonda follevod somo signiftemt develop- nenta in the theo ry of sarpling fron finite popalations mainly concontrated on the utilisatlon of muxdlfary infornation at different stagea (stratirication, sample neleetion, esttnatten, ete.) threngh the totahle oontrihutionn of Co chran, Dalentus, Des Raj, Hanger, Iandta, Lahiri, Nadow, Koop, Yates and others, These developaants gave rino ta a cunber of smpling techni gnos (systenatie simpliag, probabi1ity proportional to s1ze (PPS) nampline, strutifiod sanpling, ete,) and estisation procedures (ratto and rogrosston methods af ostinatlan) appro- priste to varloas situations in practles to estinate the population nean or total of a varleto ant the orrors of these estánates, The nost inportaat connopt of 'oost funetion' was introdueed by Haal anobis (1940) to fadge the effieiency of vsrdons ostimators per unit oost.A munber of reviova hare appeared on the developmenta in theo retical and applied rodearch on nanpling from finite populntions; the notable ones sn this direstion sre the se by Yatas (198), Cochran (1947), atophan (1948), Seng (1961), Sukaatae (1960, 66), Dalendus (1962), Murthy (1963), Vas (1974), Anong others,With the advent of various selaction procetures aa the eorrespoading estimation preceduroes, the nood was irst felt by Herrita and Thompsan (1962) to ovelve a systamatie theory of sempiing fren. ini te populations and beatdes fomalating the thoery nontly, they defined three elosses of entiastors, Later in (1856), todmhe propoaod a aniftod thoory of smpling fron Tinite pomilationa with a viev to diseasning the findamen- taa problens ef sampling within thts Crane work, Parther, God ambe (1955) has obtained the celebrated restlt that for any smple design there does not exd st a uniformly minimum variance unbiesed estimator of the population total in the class of all 1inear unbiased estimators (with scme axceptions characterised by Hamurav (1965) later, termed as 'unteluster designs'). This then, has led to the choice of estimators from a suh-class of admi ssiblo estimators. Alternatively, varlous criterin have been put forward by many others to arrive at an optimum choice, namely, (1) Bayesnesa (Codam be (1955), Hajek (1958)), (11) invari- ance and regular elass (Roy and Chakravo rti (1960))and (111) hyper-admissibility (Hamarav (1966)), to quote a few.Uging Beyes appro ach in scempling theory, 1t was first shovn by Co ahran (1946) that whenever aaxdliary infomation on a sapplatentary variate closely related to the study variate 19 available, wo can util1 ze this info rmation to formtlate a prior distribution for the varinte under study. This is now vell Imown as the super-population concept. As stated earlier, vi th the criteria of unbiasedness and mindrtan variance, in


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