Nonparametric density estimation in presence of bias and censoring

Test

Volumn 18, Issue 1, 2009, Pages 166-194

  Brunel, E ^a   Comte, F ^a   Guilloux, A ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Adaptive estimation; Biased data; Minimax rate; Nonparametric penalized contrast estimator; Right censoring

Indexed keywords

EID: 63049129232     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11749-007-0075-5     Document Type: Article

References (34)

1. A Antoniadis G Grégoire G Nason 1999 Density and hazard rate estimation for right-censored data by using wavelet methods JR Stat Soc Ser B Stat Methodol 61 63 84
2. M Asgharian CE M'Lan DB Wolfson 2002 Length-biased sampling with right censoring: an unconditional approach J Am Stat Assoc 97 201 209
3. AR Barron L Birgé P Massart 1999 Risk bounds for model selection via penalization Probab Theory Relat Fields 113 301 413
4. L Birgé P Massart 1998 Minimum contrast estimators on sieves: exponential bounds and rates of convergence Bernoulli 4 3 329 375
5. L Birgé Y Rozenholc 2006 How many bins must be put in a regular histogram ESAIM Probab Stat 10 24 45
6. E Brunel F Comte 2005 Penalized contrast estimation of hazard rate with censored data Sankhyā 67 441 475
7. Brunel E, Comte F, Guilloux A (2005) Nonparametric density estimation in presence of bias and censoring. Preprint MAP5 2005-13. http://www.math-info. univ-paris5.fr/map5/publis/titres05.html
8. Chakraborty R, Rao CR (2000) Selection biases of samples and their resolutions. In: Sen PK, Rao CR (eds) Handbook of statistics, vol 18. Elsevier, Amsterdam, pp 675-712
9. Cox DR (1969) In: Johnson, Smith (eds) New development in survey sampling. Wiley, New York
10. J de Uña-Álvarez 2002 Product-limit estimation for length-biased censored data Test 11 109 125
11. J de Una-Álvarez 2004 Nonparametric estimation under length-biased sampling and type I censoring: a moment based approach Ann Inst Stat Math 56 667 681
12. J de Una-Álvarez A Rodriguez-Casal 2006 Comparing nonparametric estimators for length-biased data Commun Stat Theory Methods 35 905 920
13. DeVore RA, Lorentz GG (1993) Constructive approximation. Springer, Berlin
14. DL Donoho IM Johnstone 1998 Minimax estimation with wavelet shrinkage Ann Stat 26 879 921
15. S Efromovich 2004 Distribution estimation for biased data J Stat Plan Inference 124 1 43
16. S Efromovich 2004 Density estimation for biased data Ann Stat 32 3 1137 1161
17. H El Barmi JS Simonoff 2000 Transformation-based density estimation for weighted distributions J Nonparametric Stat 12 861 878
18. El Ghouch A, Van Keilegom I (2006) Nonparametric regression with dependent censored data. Discussion paper. Institute of Statistics, Louvain
19. J Fan I Gijbels 1994 Censored regression: local linear approximations and their applications J Am Stat Assoc 89 560 570
20. RA Fisher 1934 The effect of methods of ascertainment upon the estimation of frequencies Ann Eugen 6 13 25
21. RD Gill Y Vardi JA Wellner 1988 Large sample theory of empirical distributions in biased sampling models Ann Stat 16 1069 1172
22. Heckman J (1985) Selection bias and self-selection. In: The new Palgrave: a dictionary of economics. MacMillan, Stockton, pp 287-296
23. MC Jones 1991 Kernel density estimation for length biased data Biometrika 78 511 519
24. SH Lo YP Mack JL Wang 1989 Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator Probab Theory Relat Fields 80 461 473
25. JS Marron J de Uña-Álvarez 2004 SiZer for length biased, censored density and hazard estimation J Stat Plan Inference 121 149 161
26. JS Marron WJ Padgett 1987 Asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples Ann Stat 15 1520 1535
27. J Mielniczuk 1985 Properties of some kernel estimators and of the adapted Loftsgarden-Quesenberry estimator of a density function for censored data Period Math Hungar 16 69 81
28. Patil GP, Rao CR (1997) The weighted distributions: a survey of their applications. In: Krishnaiah PR (ed) Applications of statistics. North-Holland, Amsterdam, pp 383-405
29. M Talagrand 1996 New concentration inequalities in product spaces Invent Math 126 505 563
30. MA Tanner WH Wong 1983 The estimation of the hazard function from randomly censored data by the kernel method Ann Stat 11 989 993
31. Y Vardi 1982 Nonparametric estimation in presence of length bias Ann Stat 10 616 620
32. M-C Wang 1999 Gap time bias in incident and prevalent cohort Stat Sinica 9 999 1010
33. CO Wu 1997 A cross-validation bandwidth choice for kernel density estimates with selection biased data J Multivar Anal 61 38 60
34. CO Wu AQ Mao 1996 Minimax kernels for density estimation with biased data Ann Inst Stat Math 48 451 467