Some Aspects of Estimation in Sampling from Finite Populations.

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)

Intoroat in the use of sapling notho ds for obtaining the statietioal data was đi soorni blo towards the and of the last contıry itsclf, but sampling then had a sOnewhat đ£fferent neening fron to-day, the prinery aifference being the abaonce of nochanian of rondondsation in the serplo seloction and the pro babilistia intorpretation of the đata collootode Tho outotanding omtributione of Mahal ano bi sy Noynan and ukhatne during the thirtics markod a furning point in the hdatory of the amling theory and opane d-up now avenues for valuable roscarchee in the theory and philosophy of . samplo survoys. It was not until tho advent of lrgo.acalo ourvoys carried out undor the guidance of Professor Hahalanobis đuring the late thirtion thtet the philosophy of offioieney per unit cost came to be realised and in its train wero axplorod nany new nothods of solection nd cstination proceduros.During tho next deoado followed Bono significant đovolopmonta in the Broapling thoory of finito populations, nadnly rolating to the upe of mupplemontary infomation at aifforent stnges, throuh the notable contributions of Coetran, Hamgem, hevita, Yatos, Madow, Delonius nnd othere. Thono dovalopmenta gave riee to a numbor of toohni quee of Bepling and ostinatian procodures approprinto to various aituations in pran tloo to ontinsto tho population total of a roal-veluod eharnoteristie dofined for the units in tho populationWith the availabllity of vriouo seleotion and the corro eponding ostimation procoduros, the noed was felt to evalve a nifled thoory of sapling and eteps in this airootion woro takon by Horvits end Thompoon (1952), Godanbo (1985), Koop (1963) and thur tiy (1063), and ooneequently genoralised 1ineur entinntore wore aleo propoacd. mder thds unified eet-up, soarch for an optimum ostinator wae ande by uovaral uthorn and tho following remtl te are avad- lablo in tio 11terature for the hono goncoua 1iner and sho antiro olana of untiasod ontd tora, for eny dosin Pt(a) non-cdatono of a uniformly ninirnra veriance (best) eatinator in the alane of all honogonooun 1iner unbianod catiaators of the populntion total (Godrunbo, 1985, Koop, 1063)(b) atrd sed bil1ty of the Horvita ehd hompeon ostimator (the He. ostimator) of the popula- tion to tel Y in (Godenbe, 1980; Roy and Chakravar ti, 1960), (o) oxctonai.on of the romilts in (n) and (b) to the etire olaca of unbiased ostinatore (Godambe md Jonhi, 1965) of the population total, (d) edat sat blity of the varianco ostinator (of the HeT. ontinator) providod br Horvits nd honpron (1982) in the entiro alaan of unbiased ontimatoro (Godmbe md Joaht, 1965), (e) non-oxintenge of the bost ostinator in the entiro elare of unbianed ostimators of the variance of tho He e. estimntor (Codanbo and Joahi, 1965).Jonhd (1965a, 1066) removod the unbiasednens condition of ostinatos end provad that tho samplo meen and the usual ratio ontinators are adnined blo in the olasn of all ostimatore for ny dosdm with roopoet to varinoo an lone function and a gonoraliantion of this remult in given by ham (Jonhi, 1968) showing the adnisei bility of thomo ostinators for eny convex- lons funotion.


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