@article{AIHPB_2003__39_2_217_0, author = {Durot, C\'ecile and Tocquet, Anne-Sophie}, 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}, volume = {39}, year = {2003}, pages = {217-240}, doi = {10.1016/S0246-0203(02)00013-4}, mrnumber = {1962134}, zbl = {1010.62032}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2003__39_2_217_0} }
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) pp. 217-240. doi : 10.1016/S0246-0203(02)00013-4. http://gdmltest.u-ga.fr/item/AIHPB_2003__39_2_217_0/
[1] Estimation of isotonic regression, in: Nonparametric Techniques in Statistical Inference, Cambridge Univ. Press, 1970, pp. 177-195. | MR 277070
,[2] Sharp asymptotics for isotonic regression, Probab. Theory Related Fields 122 (2002) 222-240. | MR 1894068 | Zbl 0992.60028
,[3] Asymptotic normality of the l1-error of the grenander estimator, Ann. Statist. 27 (1999) 1316-1347. | MR 1740109 | Zbl 1105.62342
, , ,[4] Estimation of a monotone density or monotone hazard under random censoring, Scand. J. Statist. 22 (1995) 3-33. | MR 1334065 | Zbl 0827.62032
, ,[5] Asymptotically minimax estimation of concave and convexe distribution functions, Z. Wahrsch. Verw. Gebiete 34 (1976) 73-85. | MR 397974 | Zbl 0354.62035
, ,[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] Estimation of a unimodal density, Sankhya Ser. A 31 (1969) 23-36. | MR 267677 | Zbl 0181.45901
,[8] Continuous Martingales and Brownian Motion, Springer-Verlag, 1991. | MR 1083357 | Zbl 0731.60002
, ,[9] Estimates in the invariance principle, Trudy. Inst. Mat. Sibirsk. Otdel (1972) 27-44. | MR 821751 | Zbl 0585.60044
,[10] The limit distribution of the concave majorant of an empirical distribution function, Statist. Probab. Letters 20 (1994) 81-84. | MR 1294808 | Zbl 0801.62017
,