BibTex RIS Kaynak Göster

On conditional hazard function estimate for functional mixing data

Yıl 2015, Cilt: 3 Sayı: 2, 79 - 95, 19.01.2015

Öz

This paper considers the problem of nonparametric estimation of the conditional hazard function for functional mixingdata. In particular, given a strictly stationary random variables Zi= (Xi, Yi)i∈N, we investigate a kernel estimate of the conditionalhazard function of univariate response variable Yigiven the functional variable Xi. The mean squared convergence rate is given and theasymptotic normality of the proposed estimator is proven

Kaynakça

  • I. A. Ahmad, Uniform strong convergence of the generalized failure rate estimate, Bull. Math. Statist., 17 (1976), 77-84.
  • K. Benhenni, F. Ferraty, M. Rachdi, P. Vieu, Local smoothing regression with functional data, Comput. Statist., 22 (2007), 353-369.
  • P. Besse, H. Cardot, D. Stephenson, Autoregressive forecasting of some functional climatic variations, Scand. J. Statist., 27 (2000), 673-6
  • P. Besse, J.O. Ramsay, Principal component analysis of sampled curves, Psychometrika., 51 (1986), 285-311.
  • D. Bosq, Nonparametric statistics for stochastic processes. Estimation and prediction, (Second edition). Lecture Notes in Statistics, 110, Springer-Verlag, 1998.
  • H. Cardot, F. Ferraty, P. Sarda, Functional linear model, Statist. Probab. Lett., 45 (1999), 11-22.
  • J. Damon, S. Guillas, The inclusion of exogenous variables in functional autoregressive ozone forecasting, Environmetrics., 13 (2002), 759-774.
  • F. Ferraty, A. Mas, P. Vieu, Advances in nonparametric regression for functional variables, Australian and New Zealand Journal of Statistics., 49 (2007), 1-20.
  • F. Ferraty, A. Rabhi, P.Vieu, Conditional quantiles for functional dependent data with application to the climatic El Nino phenomenon, Sankhy˜a: The Indian Journal of Statistics, Special Issue on Quantile Regression and Related Methods, 67(2) (2005), 378-3
  • F. Ferraty, A. Rabhi, P. Vieu, Estimation non param´etrique de la fonction de hasard avec variable explicative fonctionnelle, Rom. J. Pure and Applied Math., 52 (2008), 1-18.
  • F. Ferraty, P. Vieu, Non-parametric Functional Data Analysis, Springer-Verlag, New-York, 2006.
  • 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.
  • R. J. Hyndman, D. M. Bashtannyk, G. K. Grunwald, Estimating and visualizing conditional densities, J. Comput. Graph. Statist., 5 (1996), 315-336.
  • J. Li, L.T. Tran, Hazard rate estimation on random fields, Journal of Multivariate analysis. 98 (2007), 1337-1355.
  • 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.
  • E. Masry, Non-parametric regression estimation for dependent functional data: Asymptotic normality, Stoch. Process. Appl., 115 (2005), 155-177.
  • A. Quintela, Plug-in bandwidth selection in kernel hazard estimation from dependent data, Comput. Stat. Data Anal., 51 (2007), 5800-5812.
  • A. Rabhi, S. Benaissa, E. H. Hamel, B. Mechab, Mean square error of the estimator of the conditional hazard function, Appl. Math. (Warsaw)., 40(4) (2013), 405-420.
  • M. Rachdi and P. Vieu, Non-parametric regression for functional data: Automatic smoothing parameter selection, J. Stat. Plan. Inference., 137 (2007), 2784-2801.
  • J.O. Ramsay, B.W. Silverman, Functional Data Analysis, 2nd ed., Springer-Verlag, NewYork, 2005.
  • J. Rice and 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.
  • E. Rio, Th´eorie asymptotique des processus al´eatoires d´ependants, (in french). Math´ematiques et Applications., 31, Springer- Verlag, New York, 2000.
  • G. G. Roussas, Hazard rate estimation under dependence conditions, J. Statist. Plann. Inference., 22 (1989),81-93.
  • 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 and Meth., 12 (1983), 559-588.
  • L. Spierdijk, Non-parametric conditional hazard rate estimation: A local linear approach, Comput. Stat. Data Anal., 52 (2008), 2419-2434.
  • L. T. Tran, S. Yakowitz, Nearest neighbor estimators for rom fields, J. Multivariate. Anal., 44 (1993), 23-46.
  • G. S. Watson, M. R. Leadbetter, Hazard analysis.I, Biometrika., 51 (1964),175-184.

Tayeb Djebbouri1,El Hadj Hamel2and Abbes Rabhi3

Yıl 2015, Cilt: 3 Sayı: 2, 79 - 95, 19.01.2015

Öz

Kaynakça

  • I. A. Ahmad, Uniform strong convergence of the generalized failure rate estimate, Bull. Math. Statist., 17 (1976), 77-84.
  • K. Benhenni, F. Ferraty, M. Rachdi, P. Vieu, Local smoothing regression with functional data, Comput. Statist., 22 (2007), 353-369.
  • P. Besse, H. Cardot, D. Stephenson, Autoregressive forecasting of some functional climatic variations, Scand. J. Statist., 27 (2000), 673-6
  • P. Besse, J.O. Ramsay, Principal component analysis of sampled curves, Psychometrika., 51 (1986), 285-311.
  • D. Bosq, Nonparametric statistics for stochastic processes. Estimation and prediction, (Second edition). Lecture Notes in Statistics, 110, Springer-Verlag, 1998.
  • H. Cardot, F. Ferraty, P. Sarda, Functional linear model, Statist. Probab. Lett., 45 (1999), 11-22.
  • J. Damon, S. Guillas, The inclusion of exogenous variables in functional autoregressive ozone forecasting, Environmetrics., 13 (2002), 759-774.
  • F. Ferraty, A. Mas, P. Vieu, Advances in nonparametric regression for functional variables, Australian and New Zealand Journal of Statistics., 49 (2007), 1-20.
  • F. Ferraty, A. Rabhi, P.Vieu, Conditional quantiles for functional dependent data with application to the climatic El Nino phenomenon, Sankhy˜a: The Indian Journal of Statistics, Special Issue on Quantile Regression and Related Methods, 67(2) (2005), 378-3
  • F. Ferraty, A. Rabhi, P. Vieu, Estimation non param´etrique de la fonction de hasard avec variable explicative fonctionnelle, Rom. J. Pure and Applied Math., 52 (2008), 1-18.
  • F. Ferraty, P. Vieu, Non-parametric Functional Data Analysis, Springer-Verlag, New-York, 2006.
  • 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.
  • R. J. Hyndman, D. M. Bashtannyk, G. K. Grunwald, Estimating and visualizing conditional densities, J. Comput. Graph. Statist., 5 (1996), 315-336.
  • J. Li, L.T. Tran, Hazard rate estimation on random fields, Journal of Multivariate analysis. 98 (2007), 1337-1355.
  • 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.
  • E. Masry, Non-parametric regression estimation for dependent functional data: Asymptotic normality, Stoch. Process. Appl., 115 (2005), 155-177.
  • A. Quintela, Plug-in bandwidth selection in kernel hazard estimation from dependent data, Comput. Stat. Data Anal., 51 (2007), 5800-5812.
  • A. Rabhi, S. Benaissa, E. H. Hamel, B. Mechab, Mean square error of the estimator of the conditional hazard function, Appl. Math. (Warsaw)., 40(4) (2013), 405-420.
  • M. Rachdi and P. Vieu, Non-parametric regression for functional data: Automatic smoothing parameter selection, J. Stat. Plan. Inference., 137 (2007), 2784-2801.
  • J.O. Ramsay, B.W. Silverman, Functional Data Analysis, 2nd ed., Springer-Verlag, NewYork, 2005.
  • J. Rice and 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.
  • E. Rio, Th´eorie asymptotique des processus al´eatoires d´ependants, (in french). Math´ematiques et Applications., 31, Springer- Verlag, New York, 2000.
  • G. G. Roussas, Hazard rate estimation under dependence conditions, J. Statist. Plann. Inference., 22 (1989),81-93.
  • 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 and Meth., 12 (1983), 559-588.
  • L. Spierdijk, Non-parametric conditional hazard rate estimation: A local linear approach, Comput. Stat. Data Anal., 52 (2008), 2419-2434.
  • L. T. Tran, S. Yakowitz, Nearest neighbor estimators for rom fields, J. Multivariate. Anal., 44 (1993), 23-46.
  • G. S. Watson, M. R. Leadbetter, Hazard analysis.I, Biometrika., 51 (1964),175-184.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

Tayeb Djebbouri Bu kişi benim

El Hadj Hamel Bu kişi benim

Abbes Rabhi Bu kişi benim

Yayımlanma Tarihi 19 Ocak 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

APA Djebbouri, T., Hamel, E. H., & Rabhi, A. (2015). On conditional hazard function estimate for functional mixing data. New Trends in Mathematical Sciences, 3(2), 79-95.
AMA Djebbouri T, Hamel EH, Rabhi A. On conditional hazard function estimate for functional mixing data. New Trends in Mathematical Sciences. Ocak 2015;3(2):79-95.
Chicago Djebbouri, Tayeb, El Hadj Hamel, ve Abbes Rabhi. “On Conditional Hazard Function Estimate for Functional Mixing Data”. New Trends in Mathematical Sciences 3, sy. 2 (Ocak 2015): 79-95.
EndNote Djebbouri T, Hamel EH, Rabhi A (01 Ocak 2015) On conditional hazard function estimate for functional mixing data. New Trends in Mathematical Sciences 3 2 79–95.
IEEE T. Djebbouri, E. H. Hamel, ve A. Rabhi, “On conditional hazard function estimate for functional mixing data”, New Trends in Mathematical Sciences, c. 3, sy. 2, ss. 79–95, 2015.
ISNAD Djebbouri, Tayeb vd. “On Conditional Hazard Function Estimate for Functional Mixing Data”. New Trends in Mathematical Sciences 3/2 (Ocak 2015), 79-95.
JAMA Djebbouri T, Hamel EH, Rabhi A. On conditional hazard function estimate for functional mixing data. New Trends in Mathematical Sciences. 2015;3:79–95.
MLA Djebbouri, Tayeb vd. “On Conditional Hazard Function Estimate for Functional Mixing Data”. New Trends in Mathematical Sciences, c. 3, sy. 2, 2015, ss. 79-95.
Vancouver Djebbouri T, Hamel EH, Rabhi A. On conditional hazard function estimate for functional mixing data. New Trends in Mathematical Sciences. 2015;3(2):79-95.