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Consistency rates and asymptotic normality of the high risk conditional for functional data Cover

Consistency rates and asymptotic normality of the high risk conditional for functional data

Acta Universitatis Sapientiae, Mathematica
Volume 8 (2016): Issue 1 (August 2016)
By: ,   and    
Open Access
|Aug 2016
References

References

  1. [1] M. Lothaire, Combinatorics on words, Addison-Wesley, Reading, MA, 1983.
    Search in Google Scholar
  2. [2] I. A. Ahmad, Uniform strong convergence of the generalized failure rate estimate, Bull. Math. Statist., 17 (1976), 77–84.10.5109/13105
    Open DOISearch in Google Scholar
  3. [3] N. Belkhir, A. Rabhi, S. Soltani, Exact Asymptotic Errors of the Hazard Conditional Rate Kernel, J. Stat. Appl. Pro. Lett., 2 (3) (2015), 191–204.
    Search in Google Scholar
  4. [4] K. Benhenni, F. Ferraty, M. Rachdi, P. Vieu, Local smoothing regression with functional data, Comput. Statist., 22 (2007), 353–369.10.1007/s00180-007-0045-0
    Open DOISearch in Google Scholar
  5. [5] P. Besse, H. Cardot, D. Stephenson, Autoregressive forecasting of some functional climatic variations, Scand. J. Statist., 27 (2000), 673–687.10.1111/1467-9469.00215
    Open DOISearch in Google Scholar
  6. [6] P. Besse, J. O. Ramsay, Principal component analysis of sampled curves, Psychometrika, 51 (1986), 285–311.10.1007/BF02293986
    Open DOISearch in Google Scholar
  7. [7] D. Bosq, J. P. Lecoutre, Théorie de l’estimation fonctionnelle, ECONOMICA (eds), Paris, 1987.
    Search in Google Scholar
  8. [8] H. Cardot, F. Ferraty, P. Sarda, Functional linear model, Statist. Probab. Lett., 45 (1999), 11–22.10.1016/S0167-7152(99)00036-X
    Open DOISearch in Google Scholar
  9. [9] J. Damon, S. Guillas, The inclusion of exogenous variables in functional autoregressive ozone forecasting, Environmetrics, 13 (2002), 759–774.10.1002/env.527
    Open DOISearch in Google Scholar
  10. [10] P. Doukhan, Mixing: Properties and Examples, Lecture Notes in Statist. 85, Springer-Verlag, NewYork, 1994.10.1007/978-1-4612-2642-0
    Open DOISearch in Google Scholar
  11. [11] G. Estvez-Prez, A. Quintela-del-Rio, P. Vieu, Convergence rate for cross-validatory bandwidth in kernel hazard estimation from dependent samples, J. Statist. Plann. Inference., 104 (2002), 1–30.10.1016/S0378-3758(01)00245-2
    Open DOISearch in Google Scholar
  12. [12] M. Ezzahrioui, E. Ould-Saïd, Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data, Journal of Nonparametric Statistics., 20(1) (2008), 3–18.10.1080/10485250701541454
    Open DOISearch in Google Scholar
  13. [13] M. Ezzahrioui, E. Ould Saïd, Some asymptotic results of a nonparametric conditional mode estimator for functional time series data, Statist. Neerlandica., 64 (2010), 171–201.10.1111/j.1467-9574.2010.00449.x
    Open DOISearch in Google Scholar
  14. [14] F. Ferraty, A. Laksaci, P. Vieu, Estimating some characteristics of the conditional distribution in nonparametric functional models. Statist. Inference Stochastic Process, 9 (2006), 47–76.
    Search in Google Scholar
  15. [15] F. Ferraty, A. Laksaci, A. Tadj, P. Vieu, Rate of uniform consistency for nonparametric estimates with functional variables, J. Statist. Plann. and Inf., 140 (2010), 335–352.10.1016/j.jspi.2009.07.019
    Open DOISearch in Google Scholar
  16. [16] F. Ferraty, A. Mas, P. Vieu, Advances in nonparametric regression for functional variables, Australian and New Zealand Journal of Statistics, 49 (2007), 1–20.10.1111/j.1467-842X.2007.00480.x
    Open DOISearch in Google Scholar
  17. [17] F. Ferraty, A. Rabhi, P. Vieu, Estimation non-paramétrique de la fonction de hasard avec variable explicative fonctionnelle, Rev. Roumaine Math. Pures Appl., 53 (2008), 1–18.
    Search in Google Scholar
  18. [18] F. Ferraty, P. Vieu, Nonparametric functional data analysis. Springer Series in Statistics, Theory and practice, Springer, New York, 2006.
    Search in Google Scholar
  19. [19] T. Gasser, P. Hall, B. Presnell, Nonparametric estimation of the mode of a distribution of random curves, Journal of the Royal Statistical Society, Ser. B., 60 (1998), 681–691.
    Search in Google Scholar
  20. [20] J. P. Lecoutre, E. Ould-Saïd, Estimation de la densité et de la fonction de hasard conditionnelle pour un processus fortement mélangeant avec censure, C. R. Math. Acad. Sci. Paris., 314 (1992), 295–300.
    Search in Google Scholar
  21. [21] E. Liebscher, Central limit theorem for α-mixing triangular arrays with applications to nonparemetric statistics, Mathematical Methods of Statistics, 10 (2) (2001), 194–214.
    Search in Google Scholar
  22. [22] A. Mahiddine, A. A. Bouchentouf, A. Rabhi, Nonparametric estimation of some characteristics of the conditional distribution in single functional index model, Malaya Journal of Matematik (MJM), 2 (4) (2014), 392–410.10.4064/am41-4-2
    Open DOISearch in Google Scholar
  23. [23] E. Masry, Non-parametric regression estimation for dependent functional data: Asymptotic normality, Stoch. Process. Appl., 115 (2005), 155–177.10.1016/j.spa.2004.07.006
    Open DOISearch in Google Scholar
  24. [24] A. Quintela-del-Rio, Nonparametric estimation of the maximum hazard under dependence conditions, Statist. Probab. Lett., 76 (2006), 1117–1124.10.1016/j.spl.2005.12.009
    Open DOISearch in Google Scholar
  25. [25] A. Quintela-del-Rio, Plug-in bandwidth selection in kernel hazard estimation from dependent data, Comput. Stat. Data Anal., 51 (2007), 5800–5812.10.1016/j.csda.2006.10.010
    Open DOISearch in Google Scholar
  26. [26] A. Quintela-del-Rio, Hazard function given a functional variable: Nonparametric estimation under strong mixing conditions, J. Nonparametr. Stat., 20 (2008), 413–430.10.1080/10485250802159297
    Open DOISearch in Google Scholar
  27. [27] A. Rabhi, S. Soltani, A. Traore, Conditional risk estimate for functional data under strong mixing conditions, Journal of Statistical Theory and Applications, 14 (3) (2015), 301–323.10.2991/jsta.2015.14.3.7
    Open DOISearch in Google Scholar
  28. [28] M. Rachdi, P. Vieu, Non-parametric regression for functional data: Automatic smoothing parameter selection, J. Stat. Plan. Inference., 137 (2007), 2784–2801.10.1016/j.jspi.2006.10.001
    Open DOISearch in Google Scholar
  29. [29] J. O. Ramsay, B. W. Silverman, Functional Data Analysis, 2nd ed., Springer-Verlag, NewYork, 2005.10.1007/b98888
    Open DOISearch in Google Scholar
  30. [30] J. Rice, B. W. Silverman, Estimating the mean and covariance structure non-parametrically when the data are curves, J.R. Stat. Soc. Ser. B., 53 (1991), 233–243.
    Search in Google Scholar
  31. [31] E. Rio, Théorie asymptotique des processus aléatoires faiblements dépendant, Mathématiques Application, 22(3) (2000), 331–334.
    Search in Google Scholar
  32. [32] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci., 42 (1956), 43–47.10.1073/pnas.42.1.43
    Open DOISearch in Google Scholar
  33. [33] G. Roussas, Hazard rate estimation under dependence conditions, J. Statist. Plann. Inference., 22 (1989), 81–93.10.1016/0378-3758(89)90067-0
    Open DOISearch in Google Scholar
  34. [34] N. D. Singpurwalla, M. Y. Wong, Estimation of the failure rate - A survey of non-parametric methods. Part I: Non-Bayesian methods, Commun. Stat. Theory Math., 12 (1983), 559–588.10.1080/03610928308828479
    Open DOISearch in Google Scholar
  35. [35] L. Spierdijk, Non-parametric conditional hazard rate estimation: A local linear approach, Comput. Stat. Data Anal., 52 (2008), 2419–2434.10.1016/j.csda.2007.08.007
    Open DOISearch in Google Scholar
  36. [36] G. S. Watson, M. R. Leadbetter, Hazard analysis I, Biometrika, 51 (1964), 175–184.10.1093/biomet/51.1-2.175
    Open DOISearch in Google Scholar
  37. [37] G. S. Watson, M. R. Leadbetter, Hazard analysis, Sankhyã, 26 (1964), 101–116.
    Search in Google Scholar
DOI: https://doi.org/10.1515/ausm-2016-0008 | Journal eISSN: 2066-7752
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Language: English
Page range: 127 - 149
Submitted on: Nov 11, 2015
Published online: Aug 2, 2016
Published in print: Aug 1, 2016
Published by: Sapientia Hungarian University of Transylvania
In partnership with: Paradigm Publishing Services
Keywords:
almost complete convergence,
asymptotic normality,
conditional hazard function,
functional data,
nonparametric estimation
MSC:
Primary: 62F12,
Secondary: 62G20, 62M09
Related subjects:
Mathematics,
General mathematics

© 2016 Abbes Rabhi, Latifa Keddani, Yassine Hammou, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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