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Nonparametric Confidence Regions for L-Moments

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Ordered Data Analysis, Modeling and Health Research Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 149))

Abstract

Methods for constructing joint confidence regions for L-skewness and L-kurtosis are compared by Monte Carlo simulation. Exact computations can be based on variance estimators given by Elamir and Seheult (2003, Journal of Statistical Planning and Inference) and by Wang and Hutson (2013, Journal of Applied Statistics). Confidence regions can also be constructed using the bootstrap; several variants are considered. The principal conclusions are that all methods perform poorly for heavy-tailed distributions , and that even for light-tailed distributions a sample size of 200 may be required in order to achieve good agreement between nominal and actual coverage probabilities. A bootstrap method based on estimation of the covariance matrix of the sample L-moment ratios is overall the best simple choice. Among the practical results is an L-moment ratio diagram on which confidence regions for sample L-moment statistics are plotted. This gives an immediate visual indication of whether different samples can be regarded as having been drawn from the same distribution, and of which distributions are appropriate for fitting to a given data sample.

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Author information

Authors and Affiliations

  1. New York, USA

    J. R. M. Hosking

Authors
  1. J. R. M. Hosking
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Correspondence to J. R. M. Hosking .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences FO 35, University of Texas at Dallas, Richardson, Texas, USA

    Pankaj Choudhary

  2. Fordham University, New York, New York, USA

    Chaitra H. Nagaraja

  3. Southern Methodist University, Dallas, Texas, USA

    Hon Keung Tony Ng

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Hosking, J.R.M. (2015). Nonparametric Confidence Regions for L-Moments. In: Choudhary, P., Nagaraja, C., Ng, H. (eds) Ordered Data Analysis, Modeling and Health Research Methods. Springer Proceedings in Mathematics & Statistics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-25433-3_3

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