Flury, H., Hannig, J., & Smith, R. (2024). Asymptotic Theory for Estimation of the Husler-Reiss Distribution via Block Maxima Method. arXiv preprint arXiv:2405.15649v2.
This paper investigates the properties of the maximum likelihood estimator (MLE) for the dependence parameter (λ) of the Husler-Reiss distribution when using the block maxima method on a sample of bivariate normal random variables. The primary objective is to establish the asymptotic normality of the MLE and determine the optimal block size for minimizing bias and variance.
The authors utilize a theoretical framework based on the Argmax Theorem and the Lindeberg-Feller Central Limit Theorem. They first prove the existence and finiteness of the Fisher Information for the Husler-Reiss distribution. Then, they analyze the localized log-likelihood function of the MLE under the misspecified model, where the data consists of scaled maxima of bivariate normal random variables. By examining the Taylor series expansion of this function, they derive the asymptotic distribution and bias of the MLE.
This study provides a theoretical foundation for estimating the dependence parameter of the Husler-Reiss distribution using the block maxima method. The established asymptotic normality of the MLE, along with the characterization of its bias, offers valuable insights for practical applications, such as composite likelihood estimation in Brown-Resnick processes.
This research contributes significantly to the field of extreme value theory by extending existing results for univariate extreme value distributions to the bivariate case of the Husler-Reiss distribution. It provides a framework for analyzing the asymptotic properties of estimators in multivariate extreme value analysis, which is crucial for modeling and predicting extreme events in various fields like climatology, finance, and engineering.
The study focuses specifically on the Husler-Reiss distribution, which arises as the limit of bivariate normal maxima. Future research could explore extending these results to other multivariate extreme value distributions or investigate the properties of alternative estimation methods beyond maximum likelihood.
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by Hank Flury, ... at arxiv.org 10-15-2024
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