A strong invariance theorem for the tail empirical process
Annales de l'I.H.P. Probabilités et statistiques, Tome 24 (1988) no. 4, pp. 491-506.
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     author = {Mason, David M.},
     title = {A strong invariance theorem for the tail empirical process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {491--506},
     publisher = {Gauthier-Villars},
     volume = {24},
     number = {4},
     year = {1988},
     mrnumber = {978022},
     zbl = {0664.60038},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1988__24_4_491_0/}
}
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Mason, David M. A strong invariance theorem for the tail empirical process. Annales de l'I.H.P. Probabilités et statistiques, Tome 24 (1988) no. 4, pp. 491-506. http://www.numdam.org/item/AIHPB_1988__24_4_491_0/

A. Araujo and E. Giné, The Central Limit Theorem for Real and Banach Valued Random Variables, John Wiley & Sons, New York, 1980. | Zbl

B. Cooil, Limiting Multivariate Distribution of Intermediate Order Statistics, Ann. Probab., Vol. 13, 1985, pp. 469-477. | MR | Zbl

M. Csörgó and P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, Akadémai Kiadó;;;;, Budapest, 1981. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

J.H.J. Einmahl and D.M. Mason, Strong Limit Theorems for Weighted Quantile Processes, Ann. Probab., 1988 b (to appear). | MR | Zbl

W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, Third Ed., Wiley, New York, 1968. | MR | Zbl

H. Finkelstein, The Law of Iterated Logarithm for Empirical Distributions, Ann. Math. Statist., Vol. 42, 1971, pp. 607-615. | MR | Zbl

P. Gaenssler and W. Stute, Wahrscheinlichkeitstheorie, Springer-Verlag, Berlin, Heidelberg, New York, 1977. | MR | Zbl

B.R. James, A. Functional Law of the Iterated Logarithm for Weighted Empirical Distributions, Ann. Probab., Vol. 3, 1975, pp. 762-772. | MR | Zbl

J. Kiefer, Iterated Logarithm Analogues 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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

D.M. Mason, Sums of Extreme Value Processes, Preprint, 1988.

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. | MR | Zbl

S. Orey and W.E. Pruitt, Sample Functions of the N-Parameter Wiener Process, Ann. Probab., Vol. 1, 1973, pp. 138-163. | MR | Zbl

W. Philipp and W. Stout, Invariance Principles for Martingales and Sums of Independent Random Variables, Math. Z., Vol. 192, 1986, pp. 253-264. | MR | Zbl

G.R. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, John Wiley & Sons, New York, 1986.

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. | MR | Zbl