Nonparametric Interval Estimators for the Coefficient of Variation

Dongliang Wang 1 , Margaret K. Formica 2  and Song Liu 3
  • 1 Department of Public Health and Preventive Medicine, SUNY Upstate Medical University, NY, Syracuse, USA
  • 2 Department of Public Health and Preventive Medicine, SUNY Upstate Medical University, NY, Syracuse, USA
  • 3 Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, NY, Buffalo, USA
Dongliang Wang
  • Corresponding author
  • Department of Public Health and Preventive Medicine, SUNY Upstate Medical University, Syracuse, NY, USA
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, Margaret K. Formica
  • Department of Public Health and Preventive Medicine, SUNY Upstate Medical University, Syracuse, NY, USA
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  • degruyter.comGoogle Scholar
and Song Liu
  • Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, NY, USA
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  • degruyter.comGoogle Scholar

Abstract

The coefficient of variation (CV) is a widely used scaleless measure of variability in many disciplines. However the inference for the CV is limited to parametric methods or standard bootstrap. In this paper we propose two nonparametric methods aiming to construct confidence intervals for the coefficient of variation. The first one is to apply the empirical likelihood after transforming the original data. The second one is a modified jackknife empirical likelihood method. We also propose bootstrap procedures for calibrating the test statistics. Results from our simulation studies suggest that the proposed methods, particularly the empirical likelihood method with bootstrap calibration, are comparable to existing methods for normal data and yield better coverage probabilities for nonnormal data. We illustrate our methods by applying them to two real-life datasets.

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