Koml 'os-Major-Tusn 'ady approximations to increments of uniform\n empirical processes

2017/09/03 by Abdelhakim Necir, Necir, Abdelhakim
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60F17 #62G15 #62G50 #62P05 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1709.00747

openalex publication_date 2017/09/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The well-known Koml 'os-Major-Tusn 'ady inequalities [Z. Wahrsch. Verw.\nGebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] provide\nsharp inequalities to partial sums of iid standard exponential random variables\nby a sequence of standard Brownian motions. In this paper, we employ these\nresults to establish Gaussian approximations to weighted increments of uniform\nempirical and quantile processes. This approach provides rates to the\napproximations which, among others, have direct applications to statistics of\nextreme values for randomly censored data.\n

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