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References
Alexander, K.S.: Some limit theorems for weighted and non-identically distributed empirical processes. Ph. D. dissertation, M.I.T. (1982)
Alexander, K.S.: Rates of growth and sample moduli for weighted empirical processes indexed by sets. Technical report, University of Washington, Seattle (1984)
Csáki, E.: Studies on the empirical d.f. MTA III. Oszt. Közl. 23, 239–327 (in Hungarian) (1974)
Csáki, E.: Some notes on the law of the iterated logarithm for empirical distribution function. Coll. Math. Soc. János Bolyai: Limit Theorems of Probability Theory, 47–58 (1975)
Csáki, E.: On the standardized empirical distribution function. Coll. Math. Soc. János Bolyai: Nonparametric Statistical Inference, 123–138 (1982)
Einmahl, J.H.J., Ruymgaart, F.H., Wellner, J.A.: A characterization of weak convergence of weighted multivariate empirical processes. To appear in Acta Sci. Math. (Szeged) (1984)
Geffroy, J.: Contributions à la théorie des valeurs extrèmes. Publ. Inst. Statist. Univ. Paris 7/8, 37–185 (1958/1959)
Kiefer, J.: Iterated logarithm analogues for sample quantiles when pn↓0. Proc. Sixth Berkeley Sympos. Math. Statist. Probab. 1, 227–244. Univ. of California Press (1972)
Mason, D.M.: Bounds for weighted empirical distribution functions. Ann. Probab. 9, 881–884 (1981)
Mason, D.M.: Some characterizations of almost sure bounds for weighted multidimensional empirical distributions and a Glivenko-Cantelli theorem for sample quantiles. Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 505–513 (1982)
Ruymgaart, F.H., Wellner, J.A.: Growth properties of multivariate empirical processes. Report 8202, Math. Inst., Kath. Un., Nijmegen (1982)
Ruymgaart, F.H., Wellner, J.A.: Some properties of weighted multivariate empirical processes. Statist. Decisions 2, 199–223 (1984)
Shorack, G.R., Wellner, J.A.: Linear bounds on the empirical distribution function. Ann. Probab. 6, 349–353 (1978)
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Einmahl, J.H.J., Mason, D.M. Bounds for weighted multivariate empirical distribution functions. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 563–571 (1985). https://doi.org/10.1007/BF00531867
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DOI: https://doi.org/10.1007/BF00531867