On the distance between the empirical process and its concave majorant in a monotone regression framework

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 39, Issue 2, 2003, Pages 217-240

  Durot, Cécile ^a   Tocquet, Anne Sophie ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

Author keywords

Brownian motion with parabolic drift; Central limit theorem; Isotonic regression; Least concave majorant; Nonparametric regression

Indexed keywords

EID: 0037334377     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(02)00013-4     Document Type: Article

References (10)

1. H.D. Brunk, Estimation of isotonic regression, in: Nonparametric Techniques in Statistical Inference, Cambridge Univ. Press, 1970, pp. 177-195.
2. C. Durot, Sharp asymptotics for isotonic regression, Probab. Theory Related Fields 122 (2002) 222-240.
3. 1 -error of the grenander estimator, Ann. Statist. 27 (1999) 1316-1347.
4. J. Huang, J.A. Wellner, Estimation of a monotone density or monotone hazard under random censoring, Scand. J. Statist. 22 (1995) 3-33.
5. J. Kiefer, J. Wolfowitz, Asymptotically minimax estimation of concave and convexe distribution functions, Z. Wahrsch. Verw. Gebiete 34 (1976) 73-85.
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.
8. D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, 1991.
9. A.I. Sakhanenko, Estimates in the invariance principle, Trudy. Inst. Mat. Sibirsk. Otdel (1972) 27-44.
10. Y. Wang, The limit distribution of the concave majorant of an empirical distribution function, Statist. Probab. Letters 20 (1994) 81-84.