#### Date of Submission

7-28-1961

#### Date of Award

7-28-1962

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Quantitative Economics

#### Department

Research and Training School (RTS)

#### Supervisor

Rao, C. Radhakrishna (RTS-Kolkata; ISI)

#### Abstract (Summary of the Work)

In this thesis the results of the research work done by the author in the field of sample surveys are presented. Scheme problems of estimation in sampling from finite populations were taken up for reset arch. A brief summary of this thesis is given below.In chapter 1, the author has developed a generalized theory of getting unbiased estimator for a certain class of parameters in sampling from finite population. The class of parameters considered are those which can be expressed as the sum of single-valued set functions defined over a class of sets of units belonging to a finite population. A technique of generating unbiased estimators for this class of pentameter is given for any sample design. This is of importance, since so far unbiased estimators for any sample design have been suggested on ;a priory and intuitive considerations and not as a result of generating technique. It is of interest to note that a particular general estimator given by the generating technique happens to include, as particular cases, most of the estimator commonly used in practice and this estimator may be taken as a reasonable estimator! whenever there is doubt as to which estimator is to be used.The technique of interpenetrating sub-8amples, introduced by Prof. P.C.Mahalano bis as long back as 1938, has been shown to have tremendous possibilities in estimating the bias of a certain class of non-linear parametric functions. In chapter 2 is given a technique of getting (almost) unbiased estimators based on independent inter- penetrating sub-sample estimates for parametric functions which can be expressed as non-linear functions of parameters which can be unbiased estimated using the techie given in chapter 1.In chapter 3, it is shown that in case of sampling from a finite population without replacement, corresponding to any estimator based on the order of selection of the units in the sample (ordered estimator) there exists a more efficient estimator which ignores the order of selection of the uni ts in the sample (unordered estimator). The ordered estimators suggested by different authors have been improved upon using this technique.The technique of getting (almost)unbiased estimators developed in chapter 2 is applied to the case of ratio method of estimation is inefficient. The question of estimating the bias of estimators of product of several parameters is also considered.The efficiencies of short-cut methods of estimating variance and coincidence interval are considered in chapter 6. It is shown that the lose of efficiency in estimating the variance and confidence interval on the basis of independent interpenetrating sub-sample estimates decreases more rapidly for initial increases in the number of sub-samples than for further increases. The estimator of variance built up from streta sub-sample estimates is formally shown to be more efficient than that based on the sub-sample estimates pooled over atrata without any assumptions.A procedure of determining the sample size, which can be considered as more rational than the conventional procedure, has b9en suggested and A specimen table showing the sample sizes for different situations is given.

#### Control Number

ISILib-THC5977

#### Creative Commons License

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

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Murthy, M. Dr., "Some Problems of Estimation in Sampling from Finite Populations." (1962). *Doctoral Theses*. 225.

https://digitalcommons.isical.ac.in/doctoral-theses/225

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843002