Estimation of population proportion with ranked set samples in the presence of multiple concomitants

Alvandi, Amirhossein (2019) Estimation of population proportion with ranked set samples in the presence of multiple concomitants. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (9MB)

Abstract

Ranked Set Sampling (RSS) design as one of the most renowned cost-effective sampling methods, have found a wide range of applications from agriculture to medical research. This statistical approach is commonly used in situations where measuring a variable of interest is expensive and time-consuming, however, small ordered sets of sampling units can be produced utilizing some source of auxiliary information as the ranking criterion. These concomitant variables may include any easily measurable characteristic of the units such as visually assessed cytological characteristics of patients. When ranking the units in a set, it is often unfeasible to assign unique ranks to all units. To provide some flexibility, we allow declaring ties among the individuals, and utilize the tie structure data for estimation purposes. Several authors have applied this sampling method to the problem of population proportion estimation. Throughout this thesis, we discuss various estimation procedures for population proportion using Partially Rank Ordered Set (PROS) sampling method which accomplishes the tie declarations by dividing sampling units into partially ranked subsets. We also discuss an estimation procedure that use logistic regression proportion estimates for ranking the sampling units. However, the most important contribution of our research is to extend six non-parametric and maximum likelihood population proportion estimators to incorporate the ranking information obtained from multiple sources. Through extensive simulation studies, and real data analysis, we investigate the performance of eight proportion estimators under various settings of ranking quality, and tie structures among the ranks. We show the universal superiority of RSS-based estimators over their counterparts using Simple Random Sampling (SRS), and the significant improvement in the estimation efficiency by combining the tie structure information of multiple concomitant variables.

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