Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Applied Statistics Unit (ASU-Kolkata)


Chaudhuri, Arijit (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

This dissertation contains seven Chapters. The contents in the respective Chapters may be briefly recounted as follows.A topic of classical interest in survey sampling is how to ensure the existence of a uniformly non-negative (UNN) unbiased estimator for the mean square error (MSE) of a homogeneous linear estimator (HLE) for a finite survey population total. Hájek (1958), Vijayan (1975), Rao and Vijayan (1977) and Rao (1979) developed a number of results which boil down to the folowing as narrated in the monograph by Chaudhuri and Stenger (1992).If there exist non-zero constants w, and the unknown values y, of the variable of interest y be such that for a given sampling design the MSE of an HLE for the finite population total Y, the sum of yi's over all the N population units, takes the value zero if yi/wi is a constant for every i = 1,, N, then the MSE for arbitrary values of yi's can be expressed in a specific form. When the above-mentioned ;constraint; holds, then this specific MSE-form leads to a specific form of a homogencous quadratic unbiased estimator (HQUE) for the MSE if it is to have the above noted ;UNN; - property. In the particular case of the Horvitz and Thompson;s (1952) estimator the above ;constraint induces the requirement that every sample with a positive probability of selection should have a constant number of distinct units in it. When this condition is satisfied, Yates and Grundy;s (1953) variance estimator is available with simple conditions for its UNN-property;, which has been examined in the literature to be satisfied for several celebrated schemes of sampling. Two other classical variance estimators for the Horvitz and Thompson;s (1952) estimator are given by Horvitz and Thompson (1952) and Ajgaonkar (1967). But no simple results are available to ensure their ;UNN; property. Chaudhuri (2000a) has added a correction term to Yates and Grundy;s (1953) variance estimator in case the ;constraint; is relaxed giving simple conditions for the ;UNN;-property of his resulting variances estimator. In the first Chapter of this thesis (i) sampling schemes have been identified satisfying Chaudhuri;s (2000a) conditions. Certain theorems have been established to cover general HLE;s with relaxed ;constraints;. Further extensions have been implemented to cover multistage sampling and randomized response (RR) surveys relevant to this context. The details are presented in the Chapter 1 and have appeared in Chaudhuri and Pal (2002a).The Chapter 2 deals with a specific version of cluster sampling found appropriate in certain kinds of surveys in practice. In this case the samples vary in size and hence the variance estimators of the kind presented in Chapter 1 turn out relevant. We encounter a practical survey situation when there are two kinds of sampling units - some are ;small; units like ;Primary health centres; (PHC) in Indian villages and some are ;bigger; ones so called BPHC;s. Around each BPHC there are a few PHC;s that are geographically contiguous and each serves exclusive groups of villagers.


ProQuest Collection ID:

Control Number


Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Included in

Mathematics Commons