On the distributions of L p norms of weighted quantile processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 26 (1990) no. 1, pp. 65-85. 
@article{AIHPB_1990__26_1_65_0,
     author = {Cs\"org\"o, Mikl\'os and Horv\'ath, Lajos},
     title = {On the distributions of $L_p$ norms of weighted quantile processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {65--85},
     publisher = {Gauthier-Villars},
     volume = {26},
     number = {1},
     year = {1990},
     mrnumber = {1075439},
     zbl = {0699.62045},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1990__26_1_65_0/}
}
TY  - JOUR
AU  - Csörgö, Miklós
AU  - Horváth, Lajos
TI  - On the distributions of $L_p$ norms of weighted quantile processes
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1990
SP  - 65
EP  - 85
VL  - 26
IS  - 1
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPB_1990__26_1_65_0/
LA  - en
ID  - AIHPB_1990__26_1_65_0
ER  - 
%0 Journal Article
%A Csörgö, Miklós
%A Horváth, Lajos
%T On the distributions of $L_p$ norms of weighted quantile processes
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1990
%P 65-85
%V 26
%N 1
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_1990__26_1_65_0/
%G en
%F AIHPB_1990__26_1_65_0
Csörgö, Miklós; Horváth, Lajos. On the distributions of $L_p$ norms of weighted quantile processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 26 (1990) no. 1, pp. 65-85. http://archive.numdam.org/item/AIHPB_1990__26_1_65_0/

P.J. Bickel, Some contributions to the theory of order statistics, Proceedings of the Fifth Berkeley Symposium, Mathematical Statistics and Probability, Vol. 1, pp. 575-591 (University of California Press, Berkeley, California, 1967). | MR | Zbl

H. Chernoff, J. Gastwirth and M.V. Johns, Asymptotic distribution of linear combinations of order statistics with applications to estimation, Ann. Math. Statist., Vol. 38, 1967, pp. 52-72. | MR | Zbl

D.M. Chibisov, Some theorems on the limiting behaviour of empirical distribution functions, Selected Transl. Math. Statist. Prob., Vol. 6, 1964, pp. 147-156. | Zbl

M. Csörgö, Quantile Processes with Statistical Applications (S.I.A.M., Philadelphia, 1983). | MR | Zbl

M. Csörgö, S. Csörgö and L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes, Lect. Notes Stat., Vol. 33, Springer-Verlag, New York, 1966. | Zbl

M. Csörgö, S. Csörgö, L. Horváth and D.M. Mason, Weighted empirical and quantile processes, Ann. Probab., Vol. 14, 1986, pp. 31-85. | MR | Zbl

M. Csörgö, S. Csörgö, L. Horváth and P. Révész, On weak and strong approximations of the quantile process, Proc. Seventh Conf. Probab. Theory, pp. 81-95, Editura Academiei, Bucuresti, 1984. | MR | Zbl

M. Csörgö and L. Horváth, Approximations of weighted empirical and quantile processes, Stat. Probab. Lett., Vol. 4, 1986, pp. 275-280. | MR | Zbl

M. Csörgö and L. Horváth, Asymptotic representations of self-normalized sums, Probab. Math. Stat. (Wroclaw), Vol. 9, 1988 a, pp. 15-24. | MR | Zbl

M. Csörgö and L. Horváth, On the distributions of Lp norms of weighted uniform empirical and quantile processes, Ann. Probab., Vol. 16, 1988 b, pp. 142-161. | MR | Zbl

M. Csörgö and L. Horváth, On the distributions of the supremum of weighted quantile processes, Studia Sci. Math. Hung. 1989 (to appear). | MR | Zbl

M. Csörgö and D.M. Mason, On the asymptotic distribution of weighted empirical and quantile processes in the middle and on the tails, Stoch. Process. Appl., Vol. 25, 1987, pp. 57-72.

M. Csörgö and P. Révész, Some notes on the empirical distribution function and the quantile process, Colloquia Mathematica Societatis János Bolyai, 11, Limit Theorems in Probability Theory, P. RÉVÉSZ Ed., pp. 59-71, North-Holland, Amsterdam, 1975. | MR | Zbl

M. Csörgö and P. Révész, Strong approximations of the quantile process, Ann. Stat., Vol. 6, 1978, pp. 882-894. | MR | Zbl

M. Csörgö and P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981. | MR | Zbl

S. Csörgö, P. Deheuvels and D.M. Mason, Kernel estimates of the tail index of a distribution, Ann. Stat., Vol. 13, 1985, pp. 1050-1077. | MR | Zbl

S. Csörgö, E. Haeusler and D.M. Mason, The asymptotic distribution of trimmed sums, Ann. Probab., Vol. 16, 1988, pp. 672-699. | MR | Zbl

S. Csörgö, L. Horváth and D.M. Mason, What portion of the sample makes a partial sum asymptotically stable or normal?, Probability Theory and Related Fields, Vol. 72, 1986, pp. 1-16. | MR | Zbl

S. Csörgö and D.M. Mason, Central limit theorems for sums of extreme values, Math. Proc. Cambridge Philos. Soc., Vol. 98, 1985, pp. 547-558. | MR | Zbl

S. Csörgö and D.M. Mason, The asymptotic distribution of sums of extreme values from a regularly varying distribution, Ann. Probab., Vol. 14, 1986, pp. 974-983. | MR | Zbl

L. De Haan, On Regular Variation and its Application to the Weak Convergence of Sample Extremes, Math. Centre Tracts, 32, Amsterdam, 1975. | MR | Zbl

P. Deheuvels and D.M. Mason, The asymptotic behavior of sums of exponential extreme values, Bull. Sci. Math. Ser. 2, Vol. 112, 1988, pp.211-233. | MR | Zbl

R.M. Dudley, Some recent results on empirical processes, Probability in Banach Spaces III, Lect. Notes Math., Vol. 860, Springer-Verlag, New York, 1981. | MR | Zbl

R.M. Dudley and W. Philipp, Invariance principles for sums of Banach space valued random elements and empirical processes, Z. Wahrsch. Verw. Gebiete, Vol. 62, 1983, pp. 509-552. | MR | Zbl

J.H.J. Einmahl and D.M. Mason, Strong limit theorems for weighted quantile processes, Ann. Probab., Vol. 16, 1988, pp. 1623-1643. | MR | Zbl

J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978. | MR | Zbl

B.V. Gnedenko, Sur la distribution limite du temps maximum d'une série aléatoire, Annals of Math., Vol. 44, 1943, pp. 423-453. | MR | Zbl

L. Horváth, On the tail behaviour of quantile processes, Stoch. Process. Appl., Vol. 25, 1987, pp. 57-72. | MR | Zbl

G.S. Lo, A note on the asymptotic normality of sums of extreme values, J. Stat. Planning Inference, Vol. 22, 1989, pp. 127-136. | MR | Zbl

D.M. Mason, Asymptotic normality of linear combinations of order statistics with a smooth score function, Ann. Statist., Vol. 9, 1981, pp. 899-908. | MR | Zbl

D.M. Mason, Weak convergence of the weighted empirical quantile process in L2 (0,1), Ann. Probab., Vol. 12, 1984, pp. 243-255. | MR | Zbl

D.M. Mason and G.R. Shorack, Necessary and sufficient conditions for asymptotic normality of L-statistics, I.M.S. Bulletin, Vol. 17, 1988, p. 138.

N.E. O'Reilly, On the weak convergence of empirical processes in sup-norm metrics, Ann. Probab., Vol. 2, 1974, pp. 642-651. | MR | Zbl

D. Poilard, Convergence of Stochastic Processes, Springer-Verlag, New York, 1984. | MR | Zbl

R. Pyke and G.R. Shorack, Weak convergence of a two-sample empirical process and a new approach to Chernoff-Savage theorems, Ann. Math. Stat., Vol. 39, 1968, pp. 755-771. | MR | Zbl

E. Seneta, Regularly Varying Functions, Lect. Notes Math., Vol. 508, Springer-Verlag, Berlin, 1976. | MR | Zbl

R.J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980. | MR | Zbl

L.A. Shepp, Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Statist., Vol. 37, 1966, pp. 321-354. | MR | Zbl

G.R. Shorack, Convergence of quantile and spacings processes with applications, Ann. Math. Stat., Vol. 43, 1972, pp. 1400-1411. | MR | Zbl

G.R. Shorack, Weak convergence of empirical and quantile processes in sup-norm metrics via KMT constructions, Stoch. Proc. Appl., Vol. 9, 1979, pp. 95-98. | MR | Zbl

G.R. Shorack, Weak convergence of the general quantile process in ∥/q∥-metrics, I.M.S. Bulletin, Abstract 82 t-2.

G.R. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986. | MR | Zbl

S. Stigler, Linear functions of order statistics, Ann. Math. Stat., Vol. 40, 1969, pp.770- 788. | MR | Zbl

J.A. Wellner, Limit theorems for the ratio of the empirical distribution function to the true distribution function, Z. Wahrsch. verw. Gebiete, Vol. 45, 1978, pp. 73-88. | MR | Zbl