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Comparison between the rates of convergence of extremes under linear and under power normalization. (English) Zbl 1247.60030
Summary: By using the theory of the second-order regular variation, we study the rates of the weak convergence of the maximum order statistics under power normalization. The exact rates are obtained in the uniform metric and the total variation metric. The relationship between the rates of convergence under linear and under power normalization is derived. Some illustrative examples are given for comparing the rates of convergence.

60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
62E15 Exact distribution theory in statistics
62G30 Order statistics; empirical distribution functions
Full Text: DOI
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