Simultaneous Closeness Among Order Statistics to Population Quantiles

• Activity Number: 120
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Narayanaswamy Balakrishnan and Katherine Davies and Jerome P. Keating*+ and Robert L. Mason
• Companies: McMaster University and University of Manitoba and The University of Texas at San Antonio and Southwest Research Institute
• Keywords: Order Statistics ; Pitman Closeness ; Probabilities of Closeness ; Qunatiles

Abstract

In this talk, we attempt to determine among all order statistics in a random sample, which one is more frequently closest than all other order statistics to a population quantile. In this regard, we consider (or compare) all order statistics simultaneously, or concurrently, as opposed to many paired comparisons. In computing the probability with which an order statistic is most-frequently closest among all those in a sample, we are computing the simultaneous version of Pitman's measure of closeness as formulated by Blyth (JASA, 1972). We constrain our attention to location and scale parameter families and draw some conclusions about best order statistics in this sense with applications to "plotting points" and misclassification probabilities.