Abstract
Consider the maximum of independent and identically distributed random variables. The classical result says that the renormalized sample maximum converges to an extreme value distributions, under certain conditions on the distribution function. In the present paper, we shall study the uniform rate of the convergence with respect to the Kolmogorov distance in the framework of the Stein equations. Some typical examples are raised in the paper.
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This work was partially carried out under the ISM Cooperative Research Program (2017 ISM⋅CRP-5011)
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Kusumoto, H., Takeuchi, A. Remark on rates of convergence to extreme value distributions via the Stein equations. Extremes 23, 411–423 (2020). https://doi.org/10.1007/s10687-020-00380-5
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DOI: https://doi.org/10.1007/s10687-020-00380-5
Keywords
- Extreme value distributions
- Convergence rate
- The integration by parts formula
- The Stein equations
- the Kolmogorov distance