Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant |
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| Authors: | Vladimir N. Kulikov Hendrik P. Lopuhaä |
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| Affiliation: | (1) ING Financial Markets, Amsterdam, The Netherlands;(2) Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands |
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| Abstract: | We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L k -type distances. In the case of a uniform distribution, we also establish their limit distribution together with that of the supremum distance. It turns out that in the uniform case, the measures of deviation are of greater order and their limit distributions are different. |
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| Keywords: | Empirical process Least concave majorant Central limit theorem Brownian motion with parabolic drift L k distance |
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