Type of Culminating Activity
Master of Science in Mathematics
In this study we address the problem of using effective sample size (ESS) to approximate the probability distributions of order statistics from correlated data. We present these approximations and determine their accuracy through simulation studies. More often than not, correlation exists between data points in a set of data. When we use the original sample size of the data in a derivation of a model of the data, we automatically assume that each data point contains one data point's worth of information. If the data are correlated, then each data point contains less than one data point's worth of information making our assumption false. This is especially true in the case of data with a very high level of correlation. Effective sample size represents essentially how many pieces of uncorrelated information the sample would compare to and this is often much smaller than the original sample size. Here we calculate effective sample size which we then use in place of the original sample size. We use a method discussed by Thiebaux and Zwiers  for the calculation of effective sample size and show its usefulness using an application to the approximation of the probability distributions of order statistics in correlated data, and finally, we compare our results with simulated data.
McGrath, Neill, "Effective Sample Size in Order Statistics of Correlated Data" (2009). Boise State University Theses and Dissertations. Paper 32.