An assessment of modified systematic sampling designs in the presence of linear trend.
Naidoo, Llewellyn Reeve.
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Sampling is used to estimate population parameters, as it is usually impossible to study a whole population, due to time and budget restrictions. There are various sampling designs to address this issue and this thesis is related with a particular probability sampling design, known as systematic sampling. Systematic sampling is operationally convenient and efficient and hence is used extensively in most practical situations. The shortcomings associated with systematic sampling include: (i) it is impossible to obtain an unbiased estimate of the sampling variance when conducting systematic sampling with a single random start; (iii) if the population size is not a multiple of the sample size, then conducting conventional systematic sampling, also known as linear systematic sampling, may result in variable sample sizes. In this thesis, I would like to provide some contribution to the current body of knowledge, by proposing modifications to the systematic sampling design, so as to address these shortcomings. Firstly, a discussion on the measures used to compare the various probability sampling designs is provided, before reviewing the general theory of systematic sampling. The per- formance of systematic sampling is dependent on the population structure. Hence, this thesis concentrates on a specific and common population structure, namely, linear trend. A discussion on the performance of linear systematic sampling and all relative modifica- tions, including a new proposed modification, is then presented under the assumption of linear trend among the population units. For each of the above-mentioned problems, a brief review of all the associated sampling designs from existing literature, along with my proposed modified design, will then be explored. Thereafter, I will introduce a modified sampling design that addresses the above-mentioned problems in tandem, before providing a comprehensive report on the thesis. The aim of this thesis is to provide solutions to the above-mentioned disadvantages, by proposing modified systematic sampling designs and/or estimators that are favourable over its existing literature counterparts. Keywords: systematic sampling; super-population model; Horvitz-Thompson estimator; Yates' end corrections method; balanced modified systematic sampling; multiple-start balanced modified systematic sampling; remainder modified systematic sampling; balanced centered random sampling.