Post stratification is considered desirable in sample surveys for two
reasons - it reduces the mean squared error when averaged over all possible
samples, and it reduces the conditional bias when conditioned on stratum
sample sizes. The problem studied in this thesis is post stratified estimation
of a finite population mean when there is a known auxiliary variable for each
population unit.
The primary direction of the thesis follows the lines of Holt and
Smith (1979). A method is given for using the auxiliary variable in selection
of the stratum boundaries and, using this approach to determine strata, to
compare post stratified estimates with the self -weighting estimates from
the analytical and empirical points of view. Estimates studied are: the post
stratified mean, the post stratified combined ratio, and the post stratified
separate ratio. The thesis contains simulation results that explore the
distributions of the self -weighting estimates, and the post stratified estimates
using conditional and unconditional inferences. The correct coverage
properties of the confidence intervals are compared and the design effect,
i.e. the ratio of the variance of the self -weighting to the variance of post
stratified estimates, is calculated from the samples and its distribution
explored by the simulation study for several real and artificial
populations. The confidence intervals of post stratified estimates
using conditional variances had good coverage properties for each
sample configuration used, and hence the correct coverage property over
all possible samples provided that the Central Limit Theorem was applied.
The comparisons indicated that post stratification is an effective
approach when the boundaries are obtained based on proper stratification using
an auxiliary variable. Moreover it is more efficient than estimation based
on simple random sampling in reducing the mean squared error.
Finally, there is strong evidence that the post stratified estimates are
robust against poorly distributed samples, whereas empirical investigations
suggested that the self -weighting estimates are very poor when the samples are
unbalanced. / Graduation date: 1990
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/37984 |
| Date | 18 September 1989 |
| Creators | Bedier, Mostafa Abdellatif |
| Contributors | Faulkenberry, G. David |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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