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Statistics Seminar Series

Wednesday, March 7, 2007 @ 4:15PM
Location:  Kupfrian Hall, Room 109
New Jersey Institute of Technology

Some Recent Developments In Ranked Set Sampling And Their Applications

Kaushik Ghosh, Ph.D

Department of Mathematical Sciences
New Jersey Institute of Technology

In many practical problems, the variable of interest is difficult/expensive to measure but the sampling units can be easily ranked based on another related variable. For example, in studies of obesity, the variable of interest may be the amount of body fat, which is measured by Dual Energy X-Ray Absorptiometry --- a costly procedure. The surrogate variable of body mass index is much easier to work with. Ranked set sampling is a procedure of improving the efficiency of an experiment whereby one selects certain sampling units (based on their surrogate values) that are then measured on the variable of interest. In this talk, we will first discuss some results on two-sample problems based on ranked set samples. Several nonparametric tests will be developed based on the vertical and horizontal shift functions. It will be shown that the new methods are more powerful compared to procedures based on simple random samples of the same size.

When the measurement of surrogate variable is moderately expensive, in the presence of a fixed total cost of sampling, one may resort to a generalized sampling procedure called k-tuple ranked set sampling, whereby k(>1) measurements are made on each ranked set. In the second part of this talk, we will show how one can use such data to estimate the underlying distribution function or the population mean. The special case of extreme ranked set sample, where data consists of multiple copies of maxima and minima will be discussed in detail. Finally, we will briefly discuss the effect of incorrect ranking and provide an illustration using data on conifer trees.