Affiliation:
1. Djillali Liabes University , Algeria .
Abstract
Abstract
This paper deals with the conditional hazard estimator of a real response where the variable is given a functional random variable (i.e it takes values in an infinite-dimensional space). Specifically, we focus on the functional index model. This approach offers a good compromise between nonparametric and parametric models. The principle aim is to prove the asymptotic normality of the proposed estimator under general conditions and in cases where the variables satisfy the strong mixing dependency. This was achieved by means of the kernel estimator method, based on a single-index structure. Finally, a simulation of our methodology shows that it is efficient for large sample sizes.
Publisher
Polskie Towarzystwo Statystyczne
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Reference31 articles.
1. Ait Saidi, A., Ferraty, F., Kassa, P. and Vieu, P., (2005). Single functional index model for a time series. Rev. Roumaine Math. Pures Appl. 50, pp. 321–330.
2. Ait Saidi, A., Ferraty, F., Kassa, P. and Vieu, P., (2008). Cross-validated estimations in the single functional index model. Statistics. Vol. 42, No. 6, pp. 475–494.
3. Ait Saidi, A. and Mecheri, K., (2016). The conditional cumulative distribution function in single functional index model. Comm. Statist. Theory Methods. 45, pp. 4896–4911.10.1080/03610926.2014.932808
4. Arfi, M., (2013). Nonparametric Estimation for the Hazard Function. Communications in Statistics - Theory and Methods 42, pp. 2543–2550.10.1080/03610926.2011.599008
5. Attaoui, S., (2014). Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data. AStA - Advances in Statistical Analysis 98, pp. 257–286.10.1007/s10182-014-0227-3