Award Date

5-1-2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Kaushik Ghosh

Second Committee Member

Amei Amei

Third Committee Member

Hokwon Cho

Fourth Committee Member

Guogen Shan

Number of Pages

89

Abstract

With the introduction of Ranked Set Sampling (RSS), McIntyre (1952) demonstrated that using ranking information to select units for measurement can lead to estimators with reduced variance when compared to their counterparts based on a simple random sample of the same size. This is done by selecting a set of units, and without direct measurement, ranking the units in the set before identifying one unit for measurement. This ranking of the units can be done through judgement ranking (such as visual assessment), or by using a correlated auxiliary variable.

In its original form, RSS does not allow for ties when ranking and requires a screening pool of size n2. Several authors have tried to address these issues separately. In particular, Ghosh and Tiwari (2008) introduced k-Tuple Ranked Set Sampling, in which k measurements are made on each ranked set, thereby reducing the screening burden. Ozturk (2011) introduced Partially Rank-Ordered Set Sampling (PRSS) and showed that even when ties are allowed, estimators can still have lower variance when compared to their simple random sampling counterparts. Thus, the ranking burden can be reduced while still providing more efficient estimators.

In this dissertation, we generalize Ozturk’s PRSS through application of Ghosh and Tiwari’s idea of k-tuple sampling, thus addressing both screening pool size reduction as well as ranking requirements. Named k-tuple Partial Rank-Ordered Set Sampling (KPRSS), three different sampling plans are presented: Uniform KPRSS, Balanced KPRSS, and General KPRSS. Partial Rank-Ordered Set Sampling, and by extension, Ranked Set Sampling, are special cases of KPRSS.

For Uniform and Balanced KPRSS, unbiased estimators of the population mean, variance, and distribution function are derived. It is shown that the variance of the sample mean and the variance of the empirical distribution function for these sampling plans are less than or equal to the variance of their simple random sample-based counterparts. Simulation studies as well as analysis of a data set of tree heights from Platt et al. (1988) are used to illustrate these results. For General KPRSS, an estimator of the population distribution function is derived along with its asymptotic properties.

Keywords

K-tuple ranked set sampling; Partially rank-ordered set sampling; Ranked set sampling

Disciplines

Statistics and Probability

Language

English

Available for download on Friday, May 15, 2020


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