Improved inference for the generalized Pareto distribution

Abstract

The generalized Pareto distribution is commonly used to model exceedances over a threshold. In this paper we obtain adjustments to the generalized Pareto profile likelihood function using the likelihood function modifications proposed by Barndorff-Nielsen (1983), Cox and Reid (1993), Fraser and Reid (1995), Fraser et al. (1999) and Severini (1999). We consider inference on the generalized Pareto distribution shape parameter, the scale parameter being a nuisance parameter. Bootstrap-based testing inference is also considered. Monte Carlo simulation results on the finite sample performances of the usual profile maximum likelihood estimator and profile likelihood ratio test and also their modified versions is presented and discussed. The numerical evidence favors the adjusted profile maximum likelihood estimators and tests we propose. Finally, we present an empirical application.

Datasets and Code

You can find the code for the real data application here. The code for the Monte Carlo simulation is available on request.

Citation

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