L-Statistics for Repeated Measurements Data with Application to Estimation of Trimmed Means and Quantiles and Construction of Tolerance Intervals

• Activity Number: 462
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Houssein Assaad*+ and Pankaj Choudhary
• Companies: and The University of Texas at Dallas
• Keywords: Hadamard differentiable ; tolerance intervals ; quantile ; trimmed mean ; weighted empirical process ; nonparametric inference

Abstract

L-statistics are defined for repeated measures designs and are shown to be asymptotically normal by treating them as statistical functionals. Unbalanced designs are considered. The remainder term in the von Mises expansion of a Hadamard differentiable functional is shown directly to converge to zero in probability. A Bahadur representation is obtained for sample quantiles. Three statistical applications, location estimation using trimmed mean, quantile estimation, and constructing asymptotic nonparametric tolerance intervals, all in the context of repeated measurements, are given. Simulations are used to examine the asymptotic relative efficiency of trimmed mean over its normal theory counterpart and the small sample accuracy of the trimmed mean confidence intervals and tolerance intervals.