Select optimal threshold for Hill estimator
Select optimal threshold for the Hill estimator by minimising the Asymptotic Mean Squared Error (AMSE).
Hill.kopt(data, start = c(1, 1, 1), warnings = FALSE, logk = FALSE,
plot = FALSE, add = FALSE, main = "AMSE plot", ...)data |
Vector of n observations. |
start |
A vector of length 3 containing starting values for the first numerical optimisation (see |
warnings |
Logical indicating if possible warnings from the optimisation function are shown, default is |
logk |
Logical indicating if the AMSE values are plotted as a function of \log(k) ( |
plot |
Logical indicating if the AMSE values should be plotted as a function of k, default is |
add |
Logical indicating if the optimal value for k should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
See Section 4.2.1 of Albrecher et al. (2017) for more details.
A list with following components:
k |
Vector of the values of the tail parameter k. |
AMSE |
Vector of the AMSE values for each value of k. |
kopt |
Optimal value of k corresponding to minimal AMSE value. |
gammaopt |
Optimal value of the Hill estimator corresponding to minimal AMSE value. |
Tom Reynkens based on S-Plus code from Yuri Goegebeur.
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.
Beirlant J., Vynckier, P. and Teugels, J. (1996). "Tail Index Estimation, Pareto Quantile Plots, and Regression Diagnostics." Journal of the American Statistical Association, 91, 1659–1667.
data(norwegianfire) # Plot Hill estimator as a function of k Hill(norwegianfire$size[norwegianfire$year==76],plot=TRUE) # Add optimal value of k Hill.kopt(norwegianfire$size[norwegianfire$year==76],add=TRUE)
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