Abstract
A refinement of the Komlós, Major and Tusnády (1975) inequality for the supremum distance between the uniform empirical process and a constructed sequence of Brownian bridges is obtained. This inequality leads to a weighted approximation of the uniform empirical and quantile processes by a sequence of Brownian bridges dual to that recently given by M. Csoörgő, S. Csörgő, Horváth and Mason (1986). The present theory approximates the uniform empirical process more closely than the uniform quantile process, whereas the former theory more closely approximates the uniform quantile process.
Received July 1985; revised May 1986.
Research supported by the Alexander von Humboldt Foundation while visiting the University of Munich on leave from the University of Delaware.
AMS 1980 subject classifications. Primary 60F99, 60F17.
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Mason, D.M., van Zwet, W.R. (2012). A Refinement of the KMT Inequality for the Uniform Empirical Process. In: van de Geer, S., Wegkamp, M. (eds) Selected Works of Willem van Zwet. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1314-1_26
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DOI: https://doi.org/10.1007/978-1-4614-1314-1_26
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