The bootstrap methodology in statistics of extremes -- choice of optimal sample fraction
The Hill estimator \(\widehat\gamma_n=n^{-1} \sum_{i=1}^K(\ln X_{n-i:n}-\ln X_{n-k:n})\) is considered for an i.i.d. sample \(X_1\),\dots, \(X_n\). Bootstrap methodologies of the optimal choice of sample proportion \(k/n\) are discussed. The techniques of bootstrapped MSE and asymptotic MSE optimization are described. As an alternative the use of auxiliary statistics is discussed. Different approaches are compared via simulation.
scientific article; zbMATH DE number 1995752