Isotonized Estimation of Cumulative Distribution Functions from Judgment Post-Stratification Data

• Activity Number: 339
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xinlei Wang*+ and Ke Wang and Lynne Stokes
• Companies: Southern Methodist University and Southern Methodist University and Southern Methodist University
• Keywords: Ranked set sampling ; isotonic regression ; minmax ; maxmin ; empty cells

Abstract

Judgment post-stratification (JP-S) is a data collection method introduced by MacEachern, Stasny and Wolfe (2004), based on ideas similar to those in ranked set sampling. In this research, for JP-S data, we consider isotonized estimators of the cumulative density function (CDF) of a population of interest, which exploit the fact that the distributions of the judgment post-strata are often stochastically ordered. Further for JP-S data with small sample sizes, we deal with the problem of empty cells, and propose modified isotonized estimators of the CDF. All these new estimators are examined by simulation studies and illustrated with data examples.