On the distance between the empirical process and its concave majorant in a monotone regression framework
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 2, pp. 217-240. 
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     title = {On the distance between the empirical process and its concave majorant in a monotone regression framework},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {217--240},
     publisher = {Elsevier},
     volume = {39},
     number = {2},
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Durot, Cécile; Tocquet, Anne-Sophie. On the distance between the empirical process and its concave majorant in a monotone regression framework. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 2, pp. 217-240. doi : 10.1016/S0246-0203(02)00013-4. http://www.numdam.org/articles/10.1016/S0246-0203(02)00013-4/

[1] H.D. Brunk, Estimation of isotonic regression, in: Nonparametric Techniques in Statistical Inference, Cambridge Univ. Press, 1970, pp. 177-195. | MR

[2] C. Durot, Sharp asymptotics for isotonic regression, Probab. Theory Related Fields 122 (2002) 222-240. | MR | Zbl

[3] P. Groeneboom, G. Hooghiemstra, H.P. Lopuhaä, Asymptotic normality of the l1-error of the grenander estimator, Ann. Statist. 27 (1999) 1316-1347. | MR | Zbl

[4] J. Huang, J.A. Wellner, Estimation of a monotone density or monotone hazard under random censoring, Scand. J. Statist. 22 (1995) 3-33. | MR | Zbl

[5] J. Kiefer, J. Wolfowitz, Asymptotically minimax estimation of concave and convexe distribution functions, Z. Wahrsch. Verw. Gebiete 34 (1976) 73-85. | MR | Zbl

[6] V.N. Kulikov, H.P. Lopuhaä, The limit process of the difference between the empirical distribution function and its concave majorant, Manuscript in preparation, 2002.

[7] B.L.S. Prakasa Rao, Estimation of a unimodal density, Sankhya Ser. A 31 (1969) 23-36. | MR | Zbl

[8] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, 1991. | MR | Zbl

[9] A.I. Sakhanenko, Estimates in the invariance principle, Trudy. Inst. Mat. Sibirsk. Otdel (1972) 27-44. | MR | Zbl

[10] Y. Wang, The limit distribution of the concave majorant of an empirical distribution function, Statist. Probab. Letters 20 (1994) 81-84. | MR | Zbl

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