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

Cécile Durot; Anne-Sophie Tocquet

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 2, page 217-240
  • ISSN: 0246-0203

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Durot, Cécile, and 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 39.2 (2003): 217-240. <http://eudml.org/doc/77760>.

@article{Durot2003,
author = {Durot, Cécile, Tocquet, Anne-Sophie},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {isotonic regression; Brownian motion; parabolic drift; least concave majorant; central limit theorem},
language = {eng},
number = {2},
pages = {217-240},
publisher = {Elsevier},
title = {On the distance between the empirical process and its concave majorant in a monotone regression framework},
url = {http://eudml.org/doc/77760},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Durot, Cécile
AU - Tocquet, Anne-Sophie
TI - On the distance between the empirical process and its concave majorant in a monotone regression framework
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 2
SP - 217
EP - 240
LA - eng
KW - isotonic regression; Brownian motion; parabolic drift; least concave majorant; central limit theorem
UR - http://eudml.org/doc/77760
ER -

References

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  1. [1] H.D. Brunk, Estimation of isotonic regression, in: Nonparametric Techniques in Statistical Inference, Cambridge Univ. Press, 1970, pp. 177-195. MR277070
  2. [2] C. Durot, Sharp asymptotics for isotonic regression, Probab. Theory Related Fields122 (2002) 222-240. Zbl0992.60028MR1894068
  3. [3] P. Groeneboom, G. Hooghiemstra, H.P. Lopuhaä, Asymptotic normality of the l1-error of the grenander estimator, Ann. Statist.27 (1999) 1316-1347. Zbl1105.62342MR1740109
  4. [4] J. Huang, J.A. Wellner, Estimation of a monotone density or monotone hazard under random censoring, Scand. J. Statist.22 (1995) 3-33. Zbl0827.62032MR1334065
  5. [5] J. Kiefer, J. Wolfowitz, Asymptotically minimax estimation of concave and convexe distribution functions, Z. Wahrsch. Verw. Gebiete34 (1976) 73-85. Zbl0354.62035MR397974
  6. [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. Zbl1106.60034
  7. [7] B.L.S. Prakasa Rao, Estimation of a unimodal density, Sankhya Ser. A31 (1969) 23-36. Zbl0181.45901MR267677
  8. [8] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, 1991. Zbl0731.60002MR1083357
  9. [9] A.I. Sakhanenko, Estimates in the invariance principle, Trudy. Inst. Mat. Sibirsk. Otdel (1972) 27-44. Zbl0585.60044MR821751
  10. [10] Y. Wang, The limit distribution of the concave majorant of an empirical distribution function, Statist. Probab. Letters20 (1994) 81-84. Zbl0801.62017MR1294808

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