JSM 2004 - Toronto

Abstract #301738

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Activity Number: 113
Type: Contributed
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301738
Title: Jackknifing Bias of Box-type Approximation under Dependence: A Nonparametric Approach for Longitudinal Data
Author(s): Xiaofeng Wang*+ and Zhaozhi Fan and Jiayang Sun
Companies: Case Western Reserve University and University of New Hampshire and Case Western Reserve University
Address: Dept. of Statistics, CWRU, Cleveland, OH, 44106-7054,
Keywords: Box-Type approximation ; longitudinal data ; jackknife ; heteroscedastic errors ; robust analysis of variance
Abstract:

Asymptotically distribution-free rank tests have been developed for testing nonparametric hypotheses in factorial experiments when data are independent. The asymptotic null distribution developed by Brunner, Dette, and Munk (1997) for these tests is conservative when data are dependent, because the estimator of d, the degrees of freedom used in the approximation is biased. We provide a bias-corrected estimate of d using a Box-type correction. This is related to the Jackknife delete-k procedure. The choice of k is studied. The new approximation to the null distribution of these test statistics is shown to be more accurate than BDM's approximation, via analysis and simulation studies. Our methodology is applied to a longitudinal case study in epidemiology.

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