Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Research and Training School (RTS)


Basu, Debabrata (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

The work Presented here had originated from a pioneering paper by Basu1 and is essentially an extension of his ideas to different problem in sample surveys. The whole word mainly consists in deriving estimators uniformly better than those usually adopted in with replacement with replacement sampling schemes, the 'order-statistic' (distinct sample unite arranged in an ascending order of their unit-indices) forms a sufficient statistic. Therefore, if any estimator (e.g., say of the population man) does not depend on the 'order-statistic', it can be uniformly improved by the use of the Rao-blalckwell theorem. The author has not hesitated to use this powerful theorem to derive improved estimators- It T is a sufficient statistic, for any convex (downwards_ lose function, an estimator uniformly better than g(S) (where g(S) is some estimator based on the sample S) is given by E[g(S)1T]=S>ΣT g(S) p(S)/ S>Σ T p(S)The whole theais ie divided into eight chapter and two ppendioen. Che pter II hau been davoted to the problen of finting moente of dietinet uni te that appear in a aple, thie chapber haa teen very helprul in getting now roulte in subeequent ehaptere whieh vould haw been, othervia, dieioult te obtain. It may te podntod out shat it we thie ohnpter vhiah ultiantely led the uthar te write don the theute. It hae been the authorte endeavour to prent selfcontadned trea tamt of the problens dinouneod haredn. N ia for thia and for the purpoee of completens that soe problene already oonaidered y other authom, ae alno given in a stapli fied fam. TheProblems with which have been dnly oonermel, are the entdmetion of the poulatton ana ? (or total), ste aqure nd the population varianoe. The problan of finting unbiaaed entinstor of the saqure of the population mean arone whi le finding undad varianoe entiantore of the eatiatore af . The following teahnique for finding waldaad varianoe eetimtore hae been uaed- if ia an unhdased catian tor of , an unbiaaed estigtor of v(4) ie givenly2


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