Estimation and simulation of conditional hazard function in the quasi-associated framework when the observations are linked via a functional single-index structure

References

• Ait Saidi, A., Ferraty, F., Kassa, R., Vieu, P. (2005). Single functional index model for a time series. Rev. Roumaine Math. Pures Appl. 50:321–330.
   Google Scholar
• Ait Saidi, A., Ferraty, F., Kassa, R., Vieu, P. (2008a). Choix optimal du paramètre fonctionnel dans le modèle à indice fonctionnel simple. C.R. Math. Acad. Sci. Paris, Ser. I 346:217–220.
   Google Scholar
• Ait Saidi, A., Ferraty, F., Kassa, R., Vieu, P. (2008b). Cross-validated estimations in the single-functional index model. Statistics 42 (6):475–494.
   Web of Science ®Google Scholar
• Ait Saidi, A., Mecheri, K. 2016. The conditional cumulative distribution function in singlefunctional index model (accepted and to appear). Commun. Stat. Theory Methods 45 (16).
   PubMed Web of Science ®Google Scholar
• Attaoui, S., Laksaci, A., Ould Said, E. (2011). A note on the conditional density estimate in the single functional index model. Stat. Probab. Lett. 81:45–53.
   Web of Science ®Google Scholar
• Bouraine, M., Ait Saidi, A., Ferraty, F., Vieu, P. (2010). Choix optimal de l’indice Multi-fonctionnel: Methode de validation croisée. Rev. Roumaine Math. Pures Appl. 55:355–367.
   Google Scholar
• Bulinski, A., Shabanovich, E. (1998). Asymptotical behaviour of some functionals of positively and negatively dependent random field. Fundam. Appl. Math. 4:479–492.
   Google Scholar
• Delecroix, M., Hristache, M. (1999). M-estimateurs semi-paramé triques dans les modèles direction révélatrice unique. Bull. Belgian Math. Soc. Simon Stevin 6:161–185.
   Web of Science ®Google Scholar
• Douge, L. (2010). Théorèmes limites pour des variables quasi-associées hilbertiennes. Ann. I.S.U.P. 54:51–60.
   Google Scholar
• Estevèz-Pérez, G., Quintela-del-R, A., Vieu, Ph. (2002). Convergence rate for cross-validatory bandwidth in kernel hazard estimation from dependent samples. J. Stat. Plann. Inference 104:1–30.
   Web of Science ®Google Scholar
• Ferraty, F., Laksaci, A., Tadj, A., Vieu, P. (2010). Rate of uniform consistency for nonparametric estimates with functional variables. J. Stat. Plann. Inference 140:335–352.
   Web of Science ®Google Scholar
• Ferraty, F., Laksaci, A., Vieu, P. (2006). Estimating some characteristics of the conditional distribution in nonparametric functional models. Stat. Inference Stochastics Process. 9:47–76.
   Google Scholar
• Ferraty, F., Peuch, A., Vieu, P. (2003). Modèle à indice fonctional simple. C.R. Math. Acad. Sci. Paris 336:1025–1028.
   Web of Science ®Google Scholar
• Ferraty, F., Rabhi, A., Vieu, P. (2008). Estimation nonparametric de la fonction de hasard avec variable explicative fonctionnelle. Rev. Roumaine Math. Pures Appl. 53:1–18.
   Google Scholar
• Ferraty, F., Vieu, P. (2005). Nonparametric Modelling for Functional Data. Methods, Theory, Applications and Implementations. Berlin: Springer-Verlag.
   Google Scholar
• Härdle, W., Hall, P., Ichumira, H. (1993). Optimal smoothing in single-index models. Ann. Stat. 21:157–178.
   Web of Science ®Google Scholar
• Hristache, M., Juditsky, A., Spokoiny, V. (2001). Direct estimation of the index coefficient in the single-index model. Ann. Stat. 29:595–623.
   Web of Science ®Google Scholar
• Joag-Dev, K., Proschan, F. (1983). Negative association of random variables, with applications. Ann. Stat. 11:286–295.
   Web of Science ®Google Scholar
• Kallabis, R.S., Neumann, M.H. (2006). An exponential inequalityunder weak dependence. Bernoulli 12:333–350.
   Web of Science ®Google Scholar
• Laksaci, A., Boubakeur, M. (2010). Estimation nonparamétrique de la fonction de hasard avec variable explicative fonctionnelle: cas des données spatiales. Rev. Roumaine Math. Pures Appl. 55:35–51.
   Google Scholar
• Lecoutre, J.P., Ould-Said, E. (1992). Estimation de la densité et de la fonction de hasard conditionnelle pour un processus fortement mé langeant avec censure. C.R. Math. Acad. Sci. Paris 314:295–300.
   Google Scholar
• Li, J., Tran, L.T. (2007). Hazard rate estimation on random fields. J. Multivariate Anal. 98:1337–1355.
   Web of Science ®Google Scholar
• Newman, C.M. (1984). Asymptotic independence and limit theorems for positively and negatively dependent random variables. Inequalities in statistics and probability. IMS Lect. Notes-Monographs Ser. 5:127–140.
   Google Scholar
• Pitt, L. (1982). Positively correlated normal variables are associated. Ann. Probab. 10:496–499.
   Web of Science ®Google Scholar
• Quintela-del-Rio. (2008). Hazard function given of functional variable: Nonparametric estimation under strong mixing conditions. J. Nonparametr. Stat. 20:413–430.
   Web of Science ®Google Scholar
• Roussas, G. (1989). Hazard rate estimation under dependence conditions. J. Stat. Plann. Inference 22:81–93.
   Web of Science ®Google Scholar
• Shashkin, A.P. (2002). Quasi-associationfor system of Gaussian vectors. Uspehi Ma. Nauk 57 (6).
   Google Scholar
• Watson, G.S., Leadbetter, M.R. (1964). Hazard analysis. Sankhyia 26:101–116.
   Google Scholar