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SA Branch meeting: Probability-proportional-to-size ranked-set sampling from stratified populations

8 Mar 2020 1:19 PM | Marie-Louise Rankin (Administrator)

The SA Branch welcomed Professor Omer Ozturk, currently on sabbatical from Ohio State University, to our February meeting to speak on his work on probability-proportional-to-size ranked-set sampling from stratified populations. This is the topic of his current research, following on from many years of work on sampling methodology. Omer’s talk took us through a number of examples to demonstrate the value of finite sampling, particularly in agriculture and environmental science.

Motivating examples included (1) the Quarterly Agricultural Survey performed by the Ohio Agricultural Statistics Department to estimate corn yield. Due to the presence of both regular farms and ‘mega farms’ auxiliary data on the farms is required to be used to ensure an appropriate sampling scheme; (2) the US Census Bureau’s Monthly Retail Trade Survey. Size data based on the previous year’s annual revenues is assumed to be approximately proportional to the current year’s revenue and can be used to optimise sampling; and (3) the Turkey Statistical Institute estimates the total apple production in Turkey. Auxiliary data identified two sub-populations, and this was able to be used to develop a sampling scheme that increased the available information.

Omer’s work combines theory from the finite population setting, proportional-to-size (PPS) and ranked-set (RS) methodologies, and extends this to more than one population (eg, geographic regions) for a stratified PPS-RS approach. Proportional-to-size sampling requires an auxiliary variable assumed to be proportional to the outcome, and ranked-set sampling requires determining, with reasonable accuracy, the relative position of the sampled units. Omer presented results for estimating the mean, variance, and confidence intervals. Finally, he discussed methods for sample size allocation across strata including equal allocation, proportional allocation, Neyman allocation, and allocation under a fixed cost plan. Results demonstrated that stratified PPS-RS was more efficient than stratified PPS and stratified simple random sampling for all allocation procedures.

In conclusion, Omar demonstrated that ranking information induces more structure and improves the information content of the sample. This can be extended to more complex population structures such as clustered populations, with further work to be published soon. It was an entertaining and engaging presentation.

Key reference: Ozturk O & Bayramoglu Kavlak K. (2018). Model based inference using ranked set samples. Survey Methodology, 44(1): 1-16.

Author: Kylie Lange

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