FitThreshold: Threshold estimation for spliced distribution

In OpVaR: Statistical Methods for Modelling Operational Risk

Description

Given a dataset with a chosen distribution for the data in the body and another distribution in the tail, the threshold is estimated.

Usage

  fitThreshold(cell, body, tail, method)

Arguments

cell	list containing the data in the component Loss
body	list containing the data in the component Loss
tail	list containing the data in the component Loss
method	Method for the threshold estimation. In case of a GPD tail, it can be chosen between "dAMSE", "danielsson", "DK", "GH", "gomes", "hall", "Himp", "HW", "mindist", "RT"

Details

## GPD tail In case of a Generalized Pareto Function in the tail, there are several methods to estimate the threshold which are based on extreme value statistics. Most of them are based on the Asymptotic Mean Squared Error (AMSE) approach. where the asymptotic squared error

Asy E((Hill(N,k)-gamma)^2)

between the true inverse tail index gamma and the Hill-estimator is minimized: "dAMSE"", "danielsson"", "DK", "GH"", gomes", "hall", "Himp" and "HW". For further details, see tea. "RT" is a heuristic approach where the smallest order statistic k that minimizes the expression 1/k sum_i=1^k i^beta |gamma_i-median(gamma_1,...,gamma_k)| is chosen for the threshold. "mindist" minimizes the distance between the largest upper order statistics (the empirical tail) and the theoretical tail of a Pareto distribution. For further details, see tea.

Value

Returns a numeric value giving threshold fitted according the given method.

Author(s)

Christina Zou, Leonie Wicht

References

# GPD Tail:

Caeiro, F. and Gomes, M.I. (2014) On the bootstrap methodology for the estimation of the tail sample fraction. Proceedings of COMPSTAT, 545-552.

Caeiro, J. and Gomes, M.I. (2016) Threshold selection in extreme value analysis. Extreme Value Modeling and Risk Analysis:Methids and Applications, 69-86

Danielsson, J. and Ergun, L.M. and de Haan, L. and de Vries, C.G. (2016) Tail Index Estimation: Quantile Driven Threshold Selection

Danielsson, J. and Haan, L. and Peng, L. and Vries, C.G. (2001) Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of Multivariate analysis, 2, 226-248.

Drees, H. and Kaufmann, E. (1998) Selecting the optimal sample fraction in univariate extreme value estimation. Stochastic Processes and their Applications, 75(2), 149-172.

Gomes, M.I. and Figueiredo, F. and Neves, M.M. (2012) Adaptive estimation of heavy right tails: resampling-based methods in action. Extremes, 15, 463-489

Guillou, A. and Hall, P. (2001) A Diagnostic for Selecting the Threshold in Extreme Value Analysis Journal of the Royal Statistical Society, 63(2), 293-305

Hall, P. (1990) Using the Bootstrap to Estimate Mean Squared Error and Select Smoothing Parameter in Nonparametric Problems. Journal of Multivariate Analysis, 32, 177-203

Hall, P. and Welsh, A.H. (1985) Adaptive estimates of parameters of regular variation. The Annals of Statistics, 13(1), 331-341.

Reiss, R.-D. and Thomas, M. (2007) Statistical Analysis of Extreme Values: With Applications to Insurance, Finance, Hydrology and Other Fields. Birkhauser, Boston.

Examples

data(lossdat)
fitThreshold(lossdat[[1]], method="dAMSE")
  

Example output

[1] 2606

OpVaR documentation built on Sept. 8, 2021, 5:07 p.m.