BibTex RIS Cite

QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL

Year 2015, Volume: 8 Issue: 1, 1 - 14, 01.03.2015

Abstract

This paper deals with a scalar response conditioned by a functional random variable. The maingoal is to estimate nonparametrically Kernel type estimator for the conditional hazard function. Finally,asymptotic properties of this estimator are stated bias the exact expression involved in the leading terms ofthe quadratic error

References

  • Bosq, D. and Lecoutre, J. P.,(1987). Thorie de l’estimation fonctionnelle Ed. Economica.
  • Dabo-Niang, S., (2002). Estimation de la densit dans un espace de dimension inŞnie : application aux diffusions, C. R., Math., Acad. Sci. Paris, 334, 213-216.
  • Dabo-Niang, S., (2002). Sur l’estimation fonctionnelle en dimension inŞnie : Application aux diffusions,
  • Thse de Doctorat, Universit de Paris 6. Ferraty, F., Rabhi, A., Vieu P., (2005). Conditional Quantiles for Dependent Functional Data with
  • Application to the Climatic El N¨ıno Phenomenon. Sankhy¨a, 67, 378-398. Ferraty, F. and Vieu, P., (2006). Nonparametric Functional Data Analysis. Theory and Practice,Springer
  • Series in Statistics. Springer, New York. Ferraty, F., A., Rabhi, Vieu,P., (2008). Estimation nonparamtrique de la fonction de hasard avec vari- ables explicatives fonctionnelles, Revue Roumaine de mathmatique.
  • Gasser, T. and Hall, P.,Presnell, B., (1998). Nonparametric estimation of the mode of a distribution of random curves, Journal of the Royal Statistical Society, Ser. B., 60, 681-691.
  • Gefeller, O. and Michels, P., (1992). A review on smoothing methods for the estimation of the hazard rate based on kernel functions, In Y. Dodge and J. Whittaker (Eds), Computational Statistics, Physica- Verlag, 459-464.
  • Hassani, S., Sarda, P., Vieu, P., (1986). Approche non-paramtrique en thorie de la Şabilit: revue bibli- ographique, Rev. Statist. Appl., 35, 27-41.
  • Izenman, A. , (1991). Developments in nonparametric density estimation, J. Amer. Statist. Assoc., 86, 224.
  • Pascu, M. , Vaduva, M., Vaduva I., (2003). Nonparametric estimation of the hazard rate: a survey, Rev.
  • Roumaine Math. Pures Appl., 48, 173-191. Patil, P.N., Wells, M.T., Maron, J.S., (1994). Some heuristics of kernel based estimators of ratio func- tions, J. Nonparametr. Statist., 4, 203-209.
  • Ramsay, J. and Silverman, B., (2005). Functional Data Analysis, 2nd Ed., Springer Series in Statistics. Springer, New York.
  • Sarda, P. and Vieu, P., (2000). Kernel regression. In: M. Schimek (ed.), Smoothing and regression.
  • Approaches, computation and application, Wiley Series in Probability and Statistics, Wiley, New York, 70. Singpurwalla, N. and Wong, M.Y., (1983). Estimation of the failure rate - a survey of nonparametric models. Part I: Non-Bayesian methods, Comm. Statist. Theory Methods, 12, 559-588.
  • Troutman, J. L., (1996). Variatonal Calculus and Optimal Control, Springer-Verlag.
  • Vieu, P., (1991). Quadratic errors for nonparametric estimates under dependence, J.Multivariate Anal., ,324-347.
Year 2015, Volume: 8 Issue: 1, 1 - 14, 01.03.2015

Abstract

References

  • Bosq, D. and Lecoutre, J. P.,(1987). Thorie de l’estimation fonctionnelle Ed. Economica.
  • Dabo-Niang, S., (2002). Estimation de la densit dans un espace de dimension inŞnie : application aux diffusions, C. R., Math., Acad. Sci. Paris, 334, 213-216.
  • Dabo-Niang, S., (2002). Sur l’estimation fonctionnelle en dimension inŞnie : Application aux diffusions,
  • Thse de Doctorat, Universit de Paris 6. Ferraty, F., Rabhi, A., Vieu P., (2005). Conditional Quantiles for Dependent Functional Data with
  • Application to the Climatic El N¨ıno Phenomenon. Sankhy¨a, 67, 378-398. Ferraty, F. and Vieu, P., (2006). Nonparametric Functional Data Analysis. Theory and Practice,Springer
  • Series in Statistics. Springer, New York. Ferraty, F., A., Rabhi, Vieu,P., (2008). Estimation nonparamtrique de la fonction de hasard avec vari- ables explicatives fonctionnelles, Revue Roumaine de mathmatique.
  • Gasser, T. and Hall, P.,Presnell, B., (1998). Nonparametric estimation of the mode of a distribution of random curves, Journal of the Royal Statistical Society, Ser. B., 60, 681-691.
  • Gefeller, O. and Michels, P., (1992). A review on smoothing methods for the estimation of the hazard rate based on kernel functions, In Y. Dodge and J. Whittaker (Eds), Computational Statistics, Physica- Verlag, 459-464.
  • Hassani, S., Sarda, P., Vieu, P., (1986). Approche non-paramtrique en thorie de la Şabilit: revue bibli- ographique, Rev. Statist. Appl., 35, 27-41.
  • Izenman, A. , (1991). Developments in nonparametric density estimation, J. Amer. Statist. Assoc., 86, 224.
  • Pascu, M. , Vaduva, M., Vaduva I., (2003). Nonparametric estimation of the hazard rate: a survey, Rev.
  • Roumaine Math. Pures Appl., 48, 173-191. Patil, P.N., Wells, M.T., Maron, J.S., (1994). Some heuristics of kernel based estimators of ratio func- tions, J. Nonparametr. Statist., 4, 203-209.
  • Ramsay, J. and Silverman, B., (2005). Functional Data Analysis, 2nd Ed., Springer Series in Statistics. Springer, New York.
  • Sarda, P. and Vieu, P., (2000). Kernel regression. In: M. Schimek (ed.), Smoothing and regression.
  • Approaches, computation and application, Wiley Series in Probability and Statistics, Wiley, New York, 70. Singpurwalla, N. and Wong, M.Y., (1983). Estimation of the failure rate - a survey of nonparametric models. Part I: Non-Bayesian methods, Comm. Statist. Theory Methods, 12, 559-588.
  • Troutman, J. L., (1996). Variatonal Calculus and Optimal Control, Springer-Verlag.
  • Vieu, P., (1991). Quadratic errors for nonparametric estimates under dependence, J.Multivariate Anal., ,324-347.
There are 17 citations in total.

Details

Other ID JA56DC85NH
Journal Section Research Article
Authors

Naouel Belkhir This is me

Abbes Rabhi This is me

Sara Soltani. This is me

Publication Date March 1, 2015
Published in Issue Year 2015 Volume: 8 Issue: 1

Cite

APA Belkhir, N., Rabhi, A., & Soltani., S. (2015). QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL. Istatistik Journal of The Turkish Statistical Association, 8(1), 1-14.
AMA Belkhir N, Rabhi A, Soltani. S. QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL. IJTSA. March 2015;8(1):1-14.
Chicago Belkhir, Naouel, Abbes Rabhi, and Sara Soltani. “QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL”. Istatistik Journal of The Turkish Statistical Association 8, no. 1 (March 2015): 1-14.
EndNote Belkhir N, Rabhi A, Soltani. S (March 1, 2015) QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL. Istatistik Journal of The Turkish Statistical Association 8 1 1–14.
IEEE N. Belkhir, A. Rabhi, and S. Soltani., “QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL”, IJTSA, vol. 8, no. 1, pp. 1–14, 2015.
ISNAD Belkhir, Naouel et al. “QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL”. Istatistik Journal of The Turkish Statistical Association 8/1 (March 2015), 1-14.
JAMA Belkhir N, Rabhi A, Soltani. S. QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL. IJTSA. 2015;8:1–14.
MLA Belkhir, Naouel et al. “QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL”. Istatistik Journal of The Turkish Statistical Association, vol. 8, no. 1, 2015, pp. 1-14.
Vancouver Belkhir N, Rabhi A, Soltani. S. QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL. IJTSA. 2015;8(1):1-14.