A Note on the Estimation of Extreme Value Distributions Using Maximum Product of Spacings

• Activity Number: 114
• Type: Contributed
• Date/Time: Monday, August 7, 2006 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Tony Siu Tung Wong*+ and Wai K. Li
• Companies: The University of Hong Kong and The University of Hong Kong
• Keywords: generalized extreme value distribution ; generalized Pareto distribution ; maximum likelihood ; maximum product of spacings ; Moran's statistic

Abstract

The maximum product of spacings (MPS) is employed in the estimation of the Generalized Extreme Value Distribution (GEV) and the Generalized Pareto Distribution (GPD). Efficient estimators are obtained by the MPS for all ?. This outperforms the maximum likelihood estimators (MLEs) which are only valid for ?<1. It is then shown that the MPS gave estimators closer to the true parameters compared to the MLE in a simulation study. In cases where sample sizes are small, the MPS performs stably while the MLE does not. Finally, as by-product of the MPS, a goodness of fit statistics, Moran's statistic, is available for the extreme value distributions. Empirical significance levels of Moran's statistic calculated are found to be satisfactory with the desired level.