Convergence faible de la statistique linéaire de rang pour des variables aléatoires faiblement dépendantes et non stationnaires
Thèses d'Orsay, no. 251 (1989) , 382 p.
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Harel, Michel. Convergence faible de la statistique linéaire de rang pour des variables aléatoires faiblement dépendantes et non stationnaires. Thèses d'Orsay, no. 251 (1989), 382 p. http://numdam.org/item/BJHTUP11_1989__0251__P0_0/

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7.bis Harel, M., Puri, M. L. (1987), Convergence faible de la statistique sérielle linéaire de rang en condition de dépendance avec application aux séries chronologiques et processus de Markov, C.R.A.S. t. 304, série I, 583-586. | MR | Zbl

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8.bis Harel, M., Puri, M. L. (1988), Convergence faible de la statistique sérielle linéaire de rang avec des fonctions de scores et des constantes de régression non bornées en condition de mélange C.R.A.S. t. 307, série I. | MR | Zbl

9. Harel, M., Puri, M. L. (1988), Weak convergence of the simple linear rank statistic for a large class of score functions under mixing conditions in the non stationary case. Technical report, Department of Mathematics, Indiana University, 24 p.

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10.bis Harel, M., Puri, M. L. (1988), Comportement limite de la U-statistique, de la V-statistique et d'une statistique de rang à un échantillon pour des processus absolument réguliers non stationnaires. C.R.A.S. t. 306, série I, 625-628. | MR | Zbl

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12. Harel, M., Puri, M. L. (1989), Limiting behaviour of one sample rank order statistics with unbounded scores for non stationary absolutely regular processes. A paraître dans Journal of Statistical Planning and Inference. | MR | Zbl

13. Harel, M., Puri, M. L. (1989), Weak invariance of generalized U-statistics for non stationary absolutely regular processes. A paraître dans Stochastic Processes and their Applications | MR | Zbl

13.bis Harel, M., Puri, M. L. (1989), Convergence faible de la U-statistique généralisée pour des processus non stationnnaires absolument réguliers. C.R.A.S. t. 309, série I, 135-138 | MR | Zbl

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Ahmad, I. and Lin, P.E. (1980). On the Chernoff-Savage theorem for dependent random sequences. Ann. Inst. Stat. Math. 32, 211-222. | MR | Zbl | DOI

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Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York. | MR | Zbl

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Einmahl, J.H.J., Ruymgaart, F.H. and Wellner, J.A. (1984). Criteria for weak convergence of weighted multivariate empirical processes indexed by points or rectangles. Acta. Sci. Math. (Szeged).

Fears, T.R. and Mehra, K. (1974). Weak convergence of a two sample empirical process and a Chernoff-Savage theorem for ϕ -mixing sequences. Ann Stat. 2, 586-596. | MR | Zbl | DOI

Harel, M. (1980). Convergence en loi pour la topologie de Skorohod du processus empirique multidimensionnel normalisé tronqué et semi-corrigé. Lecture Notes in Mathematics. Springer Verlag, 821. 46-85. | MR | Zbl

Mehra, K.L. and Rao, M.S. (1975). Weak convergence in dq-metrics of multidimensional empirical processes. Preprint, University of Alberta. Edmonton. Canada.

Neuhaus, G. (1971). On weak convergence of stochastic processes with multidimensional time parameter. Ann Statist. 42. 1285-1295. | MR | Zbl | DOI

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Withers, C.S. (1975). Convergence of empirical processes of mixing rv's on [0,1]. Ann. Stat. 3, 1101-1108. | MR | Zbl | DOI

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Alexander, K.S. (1982). Some limit theorems for weighted and non-identically distributed empirical processes. Ph.D. Thesis, M.I.T. | MR

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Fears, T.R. and Mehra, K. (1974). Weak convergence of a two sample empirical process and a Chernoff-Savage theorem for ϕ mixing sequence. Ann. of Stat. Vol. 2. No. 3. 586-596. | MR | Zbl | DOI

Harel, M. (1980). Convergence en loi pour la topologie de Skorohod du processus empirique multidimensionnel normalisé tronqué et semi-corrigé. Lecture Notes in Mathematics. Springer Verlag, 821. 46-85. | MR | Zbl

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Rüschendorf, L. (1974). On the empirical process of multivariate, dependent random variables. Journal of Multivariate Analysis 4, 469-478. | MR | Zbl | DOI

Rüschendorf, L. (1976). Asymptotic distributions of multivariate rank order statistics. Ann. Stat. 4. 912-923. | MR | Zbl | DOI

Shorack, G.R. and Wellner, J.A. (1982). Limit theorems and inequalities for the uniform empirical process indexed by intervals. Ann. Probability 10. 639-652. | MR | Zbl

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Withers, C.S. (1975). Convergence of empirical processes of mixing rv's on [0,1]. Ann. Stat. 3. 1101-1108. | MR | Zbl

[1] S. Balacheff et G. Dupont, Normalité asymptotique des processus empiriques tronqués et des processus de rang, Lecture Notes in Mathematics, n° 821, Springer Verlag, 1980, p. 19-45. | MR | Zbl

[2] P. Billingsley, Convergence of probability Measures, Wiley, New York, 1968. | MR | Zbl

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[4] M. Harel, Convergence en loi pour la topoiogie de Skorohod du processus empirique multidimensionnel normalisé tronqué et semi-corrigé, Lecture Notes in Mathematics, n° 821, Springer Verlag, 1980, p. 46-85. | MR | Zbl

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(1) S. Balacheff et G. Dupont Sur la convergence des suites de processus multidimensionnels normalisés tronqués et mélangeants. Thèse de 3ème Cycle Université de Rouen (1979)

(2) S. Balacheff et G. Dupont Normalité asymptotique des processus empiriques tronqués et des processus de rang. Lecture Notes in Mathematics Springer Verlag (1980), n° 821 pp. 19-45. | MR | Zbl

(3) P.J. Bickel and J. Wichura Convergence criteria for multiparameter stochastic processes and some applications. Ann. of Math. Stat. Vol. 42 n° 5 pp. 1656-1670 (1971) | MR | Zbl | DOI

(4) P. Billingsley Convergence of Probability Measures, Wiley (1968). | MR | Zbl

(5) R.M. Dudley Central Limit theorems for empirical measures. Ann. Probability, 6, pp. 899-929 (1978) | MR | Zbl

(6) M. Harel Convergence en loi pour la topologie de Skorohod du processus empirique multidimensionnel normalisé tronqué et semi-corrigé Lectures Notes in Mathematics, Springer-Verlag (1980), n° 821 pp. 46-85. | MR | Zbl

(7) L. Rüschendorf On the empirical Process of Multivariate, dependent Random Variables Journal of Multivariate Analysis 4, pp. 469-478 (1974) | MR | Zbl | DOI

Ahmad, I. and P.E. Lin (1980). On the Chernoff-Savage theorem for dependent random sequences. Ann. Inst. Stat. Math. 32, 211-222. | MR | Zbl | DOI

Balacheff, S. and G. Dupont (1980). Normalité asymptotique des processus empiriques tronqués et des processus de rang. Lecture Notes in Mathematics No. 821. Springer, Berlin-New York. | MR | Zbl

Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York. | MR | Zbl

Denker, M. and U. Rösler (1985). Some contributions to Chernoff-Savage theorems. Statist. and Decision 3, 49-75. | MR | Zbl

Dudley, R.M. (1978). Central limit theorems for empirical measures. Ann. Probab. 6, 899-929. | MR | Zbl

Fears, T.R. and K. Mehra (1974). Weak convergence of two sample empirical processes and a Chernoff-Savage theorem for ϕ mixing sequence. Ann. Stat. 2 (3), 586-596. | MR | Zbl | DOI

Harel, M. (1980). Convergence en loi pour la topologie de Skorohod du processus empirique multi-dimensionnel normalisé tronqué et semi-corrigé. Lecture Notes in Mathematics No. 821. Springer, Berlin-New York. | MR | Zbl

Harel, M. (1983). Convergence pour les processus empiriques éclatés. Ann. Sci. Univ. Clermont Ferrand II. | MR | Zbl | Numdam

Harel, M. (1984). Convergence en loi pour la topologie de Skorohod éclatée du processus empirique multidimensionnel normalisé tronqué éclaté et corrigé. Statist. et Analyse des Données 9 (2), 68-91. | MR | Zbl | Numdam

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Harel, M. and M.L. Puri (1987). Weak convergence of weighted multivariate empirical processes under mixing conditions. Proceedings of the 6th Pannonian Symposium on Mathematical Statistics, Volume A: Mathematical Statistics and Probablity. Reidel, Dordrecht-Boston, 121-141. | MR | Zbl

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Mehra, K.L. and M.S. Rao (1975). Weak convergence in dq-metrics of multidimensional empirical processes. Preprint, Univ. of Alberta, Edmonton, Canada.

Neumann, N. (1982). Ein Schwaches Invarianzprinzip für den gewichteten empirischen Prozess von gleichmässig mischenden Zufalsvariablen. Ph.D. Thesis, Göttingen. | Zbl

Pyke, R. and G. Shorack (1968). Weak convergence of two sample empirical processes and a new approach of Chernoff-Savage theorems. Ann. Math. Statist. 39, 755-771. | MR | Zbl | DOI

Rüschendorf, L. (1974). Of the empirical process of multivariate, dependent random variables. J. Multivariate Anal. 4, 469-478. | MR | Zbl | DOI

Rüschendorf, L. (1976). Asymptotic distributions of multivariate rank order statistics. Ann. Statist. 4 (5), 912-923. | MR | Zbl | DOI

Ruymgaart, F.H. (1974). Asymptotic normality of non-parametric tests for independence. Ann. Statist. 2 (5), 892-910. | MR | Zbl | DOI

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Van Zuijlen, M.C. (1976). Some properties of the empirical distribution function in the non-i.i.d. case. Ann. Statist. 4 (2), 406-408. | MR | Zbl

Withers, C.S. (1975). Convergence of empirical processes of mixing rv's on [0,1]. Ann. Statist. 3 (5), 1101-1108. | MR | Zbl | DOI

[1] S. Balacheff et G. Dupont, Normalité asymptotique des processus empiriques tronqués et de processus de rang, Lecture Notes in Mathematics, Springer Verlag, n° 821, 1980, p. 19-45. | MR | Zbl

[2] M. Harel, Convergence en loi pour la topologie de Skorohod du processus empirique multidimensionnel tronqué et semi-corrigé, Lecture Notes in Mathematics, Springer Verlag, n° 821, 1980, p. 46-85. | MR | Zbl

[3] M. Harel, Convergence en loi pour la topologie de Skorohod éclatée du processus empirique multidimensionnel tronqué éclaté et corrigé, Stat. et An. des données, 9, n° 2, 1984. | MR | Zbl | Numdam

Ahmad, I. and Lin, P.E. (1980). On the Chernoff-Savage theorem for dependent random sequences. Ann. Inst. Stat. Math. 32, 211-222. | MR | Zbl | DOI

Balacheff, S. and Dupont, G. (1980). Normalité asymptotique des processus empiriques tronqués et des processus de rang. Lectures Notes In Mathematics. Springer Verlag, n° 821. | MR | Zbl

Billingsley, P. (1968). Convergence probability measures. Wiley. | MR | Zbl

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Harel, M. (1980). Convergence en loi pour la topologie de Shorohod du processus empirique multidimensionnel normalisé tronqué et semi-corrigé. Lectures Notes In Mathematics. Springer Verlag n° 821. | MR | Zbl

Harel, M. (1983). Convergence pour les processus empirique éclatés. Ann. Scient. de l'Université de Clermont Ferrand II. | MR | Zbl | Numdam

Harel, M. (1984). Convergence en loi pour la topologie de Shorohod éclatée du processus empirique multidimensionnel normalisé tronqué éclaté et corrigé. Statistique et Analyse des données, n° 2, vol. 9. | MR | Zbl | Numdam

Harel, M. (1985). Weak convergence of multidimensional rank statistics in ϕ mixing condition. Submitted to Journal of Statistical Planning and Inference. | MR | Zbl

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