A strong invariance theorem for the tail empirical process

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1. A. Araujo and E. Giné, The CentralLimit Theorem for Real and Banach Valued Random Variables, John Wiley & Sons, New York, 1980. Zbl0457.60001
2. B. Cooil, Limiting MultivariateDistribution of Intermediate Order Statistics, Ann. Probab., Vol. 13, 1985, pp. 469-477. Zbl0572.62024MR781417
3. M. Csörgó and P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, Akadémai Kiadó;;;;, Budapest, 1981. Zbl0539.60029MR666546
4. M. Csörgó and D.M. Mason, On the Asymptotic Distribution of Weighted Uniform Empirical and Quantile Processes in the Middle and on the Tails, Stochastic Process. Appl., Vol. 21, 1985, pp. 119-132. Zbl0584.62025MR834992
5. J.H.J. Einmahl and D.M. Mason, Laws of the Iterated Logarithm in the Tails for Weighted Uniform Empirical Processes, Ann. Probab., Vol. 16, 1988 a, pp. 126-141. Zbl0652.60038MR920259
6. J.H.J. Einmahl and D.M. Mason, Strong Limit Theorems for Weighted Quantile Processes, Ann. Probab., 1988 b (to appear). Zbl0659.60052MR958207
7. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, Third Ed., Wiley, New York, 1968. Zbl0155.23101MR228020
8. H. Finkelstein, The Law of Iterated Logarithm for Empirical Distributions, Ann. Math. Statist., Vol. 42, 1971, pp. 607-615. Zbl0227.62012MR287600
9. P. Gaenssler and W. Stute, Wahrscheinlichkeitstheorie, Springer-Verlag, Berlin, Heidelberg, New York, 1977. Zbl0357.60001MR501219
10. B.R. James, A. FunctionalLaw of the Iterated Logarithm for Weighted Empirical Distributions, Ann. Probab., Vol. 3, 1975, pp. 762-772. Zbl0347.60030MR402881
11. J. Kiefer, Iterated LogarithmAnalogues for Sample Quantiles when pn↓0, Proceedings Sixth Berkeley Symp. Math. Statist. Probab., Vol. I, 1972, pp. 227-244, Univ. of California Press, Berkeley, Los Angeles. Zbl0264.62015MR402882
12. J. Komlós, P. Major and G. Tusnády, An Approximation of Partial Sums of Independent rv's and the Sample df, I, Z. Wahrsch. verw. Gebiete, Vol. 32, 1975, pp. 111-131. Zbl0308.60029MR375412
13. T.L. Lai, Reproducing Kernel Hilbert Spaces and the Law of the Iterated Logarithm for Gaussian Processes, Z. Wahrsch. verw. Gebiete, Vol. 29, 1974, pp. 7-19. Zbl0272.60024MR368121
14. P. Major, Approximations of Partial Sums of i.i.d.r.v.s. when the Summands Have Only Two Moments, Z. Wahrsch. verw. Gebiete, Vol. 35, 1976, pp. 221-229. Zbl0338.60032MR415744
15. D.M. Mason, Sums of Extreme Value Processes, Preprint, 1988. 
16. D.M. Mason and W.R. Van Zwet, A Refinement of the KMT Inequality for the Uniform Empirical Process, Ann. Probab., Vol. 15, 1987, pp. 871-884. Zbl0638.60040MR893903
17. S. Orey and W.E. Pruitt, Sample Functions of the N-Parameter Wiener Process, Ann. Probab., Vol. 1, 1973, pp. 138-163. Zbl0284.60036MR346925
18. W. Philipp and W. Stout, Invariance Principles for Martingales and Sums of Independent Random Variables, Math. Z., Vol. 192, 1986, pp. 253-264. Zbl0601.60033MR840828
19. G.R. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, John Wiley & Sons, New York, 1986. Zbl1170.62365
20. M.J. Wichura, Some Strassen-Type Laws of the Iterated Logarithm for Multiparameter Stochastic Processes with Independent Increments, Ann. Probab., Vol. 1, 1973, pp. 272- 296. Zbl0288.60030MR394894

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