Abstract
In stratified sampling when only one unit is selected from each stratum, the estimation of variance by customary methods becomes impossible. Various attempts have been made to solve this problem. It has been shown in this dissertation that some of them have poor stability while other can negative, an undesirable property of a variance estimator. Among the procedures suggested in the literature, it is shown that the method of Hartley et al. is best. The maximum likelihood estimator is obtained for the first time with some mild assumptions. This estimator is necessarily positive and has optimal properties. Asymptotic behavior, when the number of strata becomes large, is also studied. Some results given in the paper by Hartley and Rao 'A new estimation theory for sample surveys' are proved here and the variance of the regression type estimator is obtained. An attempt has been made to extend the results when two population parameters for concomitant variables are known.
Katiyar, Anand Singh (1969). Contributions to the stability of variance estimators and the regression estimator. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -174611.