Variance Estimation for L-Moments and L-Comoments

• Activity Number: 465
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics
• Author(s): Jonathan R.M. Hosking*+
• Companies: IBM Research
• Keywords: L-moments ; goodness of fit ; graphical methods

Abstract

Variance estimates for sample L-moment and L-comoment statistics are important for construction of confidence regions that provide simple indicators of the accuracy of the computed results and formal comparisons of sample statistics with population values that are expected under hypotheses concerning the distributions from which the samples were drawn. Unbiased estimators of variance have been provided by Elamir and Seheult; I show that in small samples these estimators often fail to give variance matrices that are positive definite. I consider alternative methods of variance estimation, including bootstrap methods (parametric and nonparametric)., empirical likelihood, and sample-based estimators of asymptotic covariance matrices of L-moments and L-moment ratios. Recommendations for methods that perform well in practice will be given. 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.