#### Date of Submission

12-28-1993

#### Date of Award

12-28-1994

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Computer Science

#### Department

Applied Statistics Unit (ASU-Kolkata)

#### Supervisor

Chaudhuri, Arijit (ASU-Kolkata; ISI)

#### Abstract (Summary of the Work)

We consider estimating the total Y of a variable y defined on a survey population. The survey is complex only in the sense that we admit sample selection with arbitrary probabilities. Our 'analysis' consists in examining efficacies of conf Idence intervals for the For this we need point estimators and or mean square error (MSE) variance { estimators, respectively say, total. the corresponding e and v. The distribution, resulting from repeated sampling, of the pivotal quantity d = (e-Y)/V 1s supposed to approximate that of standard normal deviate t or of Students t with (n-1) degrees of freedom, assuming large sample size n. We will consider three general situations, namely when we presume that (1) direct responses (DR) are available from sam individuals, (11) no direct but only randomized responses (RR) heay be gathered and (111) there may be positive probability of nonresponee (NR) from at least some individuals sampled. In such cases + consider deriving new choices of (e, v)s as alternatives to those existing in the current literature.The thesis consists of eight chapters. Throughout the first seven of them we postulate a super-population model envisaging a linear regression of y on an auxiliary variable x. Our plan is to make use of the model in choosing appropriate vs, though es may or may not be model-assisted. For a chosen e we consider the design-based MSE or an approximation of it. Every e we consider is either design-unblased or asymptotically design-unblased (ADU) in the sense of Brewer (1979) and SÃ¤rndal (1980). The asymptotic approach of Fuller and Isaki (1981) and Isaki and Fuller (1982), however is nowhere followed in this thesis. unless we refer to the recent text by Wolter (1985) that deals w* Discussion will not be complete variance estimation which also forms a principal endeavour on our p In this thesis.To utilize both the design and the model in the choice of v we draw inspiration from the works of Brewer and Hanif (1983), Kunar, Gupta and Agarwal (1985), Brewer (1990) and Kott (1990a). Their approach is to consider the "model-based expectation" of (1) the design-based expectation of (e-Y)2 and we intend first to extend it by permitting approximation of (1). Denoting thia expeciation by, say M, their procedures give a v such that the ' mode1-expeciailon of the design-expectation of v equals M. Kotts procedure goes a step v. equals Novelty in our approach is that we further in that the model-expectation of the model-expectation of (e-Y)2. find it necessary and useful to replace design-expectation in this context by asymptotic design-expectation in Brewers sense. This modificatlon leads to a series of alternative choices. This necessitates investigation of their efficacles ralative to their predecessors. In particular we also consider estimators for totals of y for specific domains. Necessary adjustments are made to cover randomized responses and (b) non-responses.

#### Control Number

ISILib-TH237

#### 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

Mitra, Joydip Dr., "Model and Design-Based Analysis of Complex Surveys." (1994). *Doctoral Theses*. 232.

https://digitalcommons.isical.ac.in/doctoral-theses/232

## 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:28843010