Date of Award


Degree Type


Degree Name



Mathematics and Statistics






Part One (Chapters 2-7) of the thesis illustrates mainly the use of auxiliary information in effecting certain transformations for improving the design/estimation strategies in sample surveys. A new product-type estimator which is complementary to the usual ratio estimator, in a certain sense, is proposed in Chapter 2. A transformation which permits the use of the product method in place of the more commonly used ratio method is discussed in the next chapter. One resulting convenience is that the bias and mean squared error of the estimator have closed form expressions, unlike that for the ratio estimator. Chapter 4 develops a change of origin for the study variate in order to improve the precision of the estimates under varying probability sampling. A change of origin under ratio method of estimation and a change of scale under the difference method are also examined. Raj (1965) has proposed a two-phase pps selection scheme in the absence of information on the auxiliary variate, but when information on some other variate is available. This also requires the knowledge of a certain parameter. Chapter 5 suggests an alternative two-phase procedure not requiring the knowledge of this parameter. Auxiliary variates in surveys are occasionally positive and negative valued. This introduces difficulties in ratio and product methods of estimation and in pps sampling. Chapter 6 outlines two simple methods of dealing with the situation: stratification by sign of the auxiliary variate and transformation by simple translation. For the purposes of illustration simple random sampling without replacement and probability proportional to size sampling with replacement are assumed. Finally, the scope for some future work is indicated in Chapter 7. Part Two (Chapters 8-9) of the thesis is a brief report on a sample survey conducted during 1980-81 to assess the transition of rural people to modern ways of life in the Karnataka State in South India.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1982 .S724. Source: Dissertation Abstracts International, Volume: 43-07, Section: B, page: 2235. Thesis (Ph.D.)--University of Windsor (Canada), 1982.