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The asymptotic distribution of weighted empirical distribution functions. (English) Zbl 0504.62021

MSC:
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions
60F05 Central limit and other weak theorems
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[1] Balkema, A.; de Haan, L., Limit laws for order statistics, Coll. math. soc. János bolyai, 17-22, (1974), Limit Theorems of Probability Theory
[2] Durbin, J., Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the kolmogorov—smirnov test, J. appl. probab., 8, 431-453, (1971) · Zbl 0225.60037
[3] Eicker, F., The asymptotic distribution of the suprema of the standardized empirical processes, Ann. statist., 7, 116-138, (1979) · Zbl 0398.62014
[4] Jaeschke, D., The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals, Ann. statist., 7, 108-115, (1979) · Zbl 0398.62013
[5] Loève, M., Probability theory I, (1977), Springer New York · Zbl 0359.60001
[6] Mason, D., Bounds for weighted empirical distribution functions, Ann. probab., 9, 881-884, (1981) · Zbl 0478.60036
[7] O’Reilly, N., On the weak convergence of empirical processes in sup-norm metrics, Ann. probab., 2, 642-651, (1974) · Zbl 0301.60007
[8] Pyke, R., The supremum and infinum of the Poisson process, Ann. math. statists, 30, 568-579, (1959)
[9] Shorack, G., Functions of order statistics, Ann. math. statist., 43, 412-427, (1972) · Zbl 0239.62037
[10] Steck, G., Rectangular probabilities for uniform order statistics and the probability that the empirical distribution function lies between two distribution functions, Ann. math. statist., 42, 1-11, (1971) · Zbl 0221.62013
[11] Wellner, J., Distributions related to linear bounds for the empirical distribution function, Ann. statist., 5, 1003-1016, (1977) · Zbl 0368.62027
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