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Hazard function given a functional variable: Non-parametric estimation under strong mixing conditions

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  • Alejandro Quintela-Del-Río

Abstract

We study here the kernel type, non-parametric estimation of the conditional hazard function, based on a sample of functional dependent data. The almost complete convergence of the conditional hazard estimate is easily derived using the properties referred by Ferraty et al for the conditional distribution and conditional density estimates. The asymptotic bias and variances of the three estimates (conditional density, distribution and hazard) are calculated and compared with the results obtained in p-dimensional non-parametric kernel estimation. The asymptotic normality is established for the three mentioned estimates. Finally, an application to an earthquake data set is made.

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  • Alejandro Quintela-Del-Río, 2008. "Hazard function given a functional variable: Non-parametric estimation under strong mixing conditions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(5), pages 413-430.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:413-430
    DOI: 10.1080/10485250802159297
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    References listed on IDEAS

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    1. Xiaohong Chen & Oliver Linton & Peter M Robinson, 2001. "The Estimation of Conditional Densities," STICERD - Econometrics Paper Series 415, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    Cited by:

    1. Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    2. Zhang, Zhen & Müller, Hans-Georg, 2011. "Functional density synchronization," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2234-2249, July.
    3. Han-Ying Liang & Elias Ould Saïd, 2018. "A weighted estimator of conditional hazard rate with left-truncated and dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 155-189, February.
    4. Kamal Boukhetala & Jean-François Dupuy, 2019. "Modélisation Stochastique et Statistique Book of Proceedings," Post-Print hal-02593238, HAL.
    5. Timmermans, Catherine & Delsol, Laurent & von Sachs, Rainer, 2013. "Using Bagidis in nonparametric functional data analysis: Predicting from curves with sharp local features," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 421-444.

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