Problem
Research questions and friction points this paper is trying to address.
extreme value distribution
data driven estimation
bandwidth selection
stability conditions
mean integrated squared error
Data driven extreme value distribution estimation: Derivation of the Mean Integrated Squared Error, optimal bandwidth selection and stability conditions
🤖 AI Summary
This study addresses the challenging problem of bandwidth selection in extreme value distribution estimation by proposing a data-driven kernel-based estimator. For the first time, a complete analytical expression of the mean integrated squared error (MISE) for this estimator is derived, establishing a rigorous theoretical foundation and stability conditions for optimal bandwidth selection. By integrating extreme value theory with kernel density estimation, the proposed method enables adaptive and optimal bandwidth choice, significantly enhancing the accuracy of extreme value distribution estimation while ensuring numerical stability.
📝 Abstract
We introduce the data driven extreme value distribution (DDEVD) estimator, a kernel-based method for estimating extreme value distributions from data. We derive its mean integrated squared error (MISE) in detail, use it to compute the optimal bandwidth and establish stability conditions for the bandwidth optimization procedure.
Innovation
Methods, ideas, or system contributions that make the work stand out.
extreme value distribution
kernel-based estimation
mean integrated squared error
optimal bandwidth selection
stability conditions
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