Article Sidebar

Download
PDF
Statistic
Read Counter : 507 Download : 417

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

In this paper, we study a smooth estimator of the conditional hazard rate function in the censorship model when the data exhibit some dependence structure. We show, under some regularity conditions, that the kernel estimator of the conditional hazard rate function suitably normalized is asymptotically normally distributed.

Keywords

Association Asymptotic normality Censored data Conditional hazard rate function Kaplan-Meier estimator kernel estimator

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
Dhiabi, S., & Sadki, O. (2023). Asymptotic Normality of the Conditional Hazard Rate Function Estimator for Right Censored Data under Association. Pakistan Journal of Statistics and Operation Research, 19(1), 115-130. https://doi.org/10.18187/pjsor.v19i1.3740
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Adjoudj L. and Tatachak A. (2019) Conditional Quantile Estimation for Truncated and Associated Data, Communications in Statistics - Theory and Methods, 48:18, 4598-4641.
  2. Bulinski, A. (1996). On the Convergence Rates in the Central Limit Theorem for Positively and Negatively Dependent Random Fields. In Probability Theory and Mathematical Statistics, eds. I.A. Ibragimov and A. Yu. Zaitsev, Netherlands: Gordan and Breach, pp. 3-14.
  3. Bulinski, A. and Shashkin, A. (2007). Limit Theorems for Associated Random Fields and Related Systems. Advanced Series on Statistical Science& Applied Probability(Vol. 10),Hackensack, NJ: WorldScientific Publishing.
  4. Cai, Z. and Roussas, GG. (1998). Kaplan-Meier Estimator under Association. Journal of Multivariate Analysis, 67, 318-348.
  5. Diallo, A. and Louani, D. (2013). Moderate and Large Deviation Principles of the Hazard Rate Function Kernel Estimator Under Censoring. Statistics and Probability Letters, 83, 735-743.
  6. Djelladj W.and Tatachak A.(2019). Strong uniform consistency of a kernel conditional quantile estimator for
  7. censored and associated data. Hacettepe Journal of Mathematics and Statistics 48, 290-311.
  8. Esary, J. Proschan, F. and Walkup, D. (1967). Association of Random Variables with Applications. Annals of Mathematical Statistics, 38, 1466-1476.
  9. Ferraty, F. Rabhi, A. and Vieu, P. (2008). Estimation non Paramétrique de la Fonction de Hasard avec Variable Explicative Fonctionnelle. Rev. Roumaine Math. Pures Appl., 53, 118.
  10. Ferrani, Y. Ould Saïd, E. and Tatachak, A. (2016). On Kernel Density and Mode Estimates for Associated and Censored Data. Communication in Statistics. Theory and Methods,45, 1853-1862.
  11. Gàmiz, M. Janys, L. Martinez-Miranda, M. and Nielsen J.P. (2013). Bandwidth Selection in Marker Dependent Kernel Hazard Estimation. Computational Statistics and Data Analysis,68, 155-169.
  12. Gheliem A. and Guessoum Z. (2022) .Simulating the behavior of a kernel M-estimator for left-truncated and associated model, Communications in Statistics - Simulation and Computation, DOI:
  13. 10.1080/03610918.2022.2075897
  14. Gonzàlez-Manteiga, W. Cao, R. and Marron, J.S. (1996). Bootstrap Selection of The Smoothing Parameter in non Parametric Hazard Rate Estimation. Journal of the American Statistical Association, 91, 1130-1140.
  15. Guessoum, Z. Ould-Saïd, E. Sadki, O. and Tatachak, A. (2012). A Note on the Lynden-Bell Estimator under Association. Statistics and Probability Letters, 82, 1994-2000.
  16. Izenman, A. (1991). Developments in Nonparametric Density Estimation. Journal of the American Statistical Association,86, 205-224.
  17. Kaplan, P. and Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53, 457-481.
  18. Lecoutre, J.P. and Ould-Saïd, E. (1995). Hazard Rate Estimation for Strong-Mixing and Censored Processes. Journal of Nonparametric Statistics, 5(1), 83-89.
  19. Lemdani, M. and Ould Saïd, E. (2007). Asymptotic Behavior of the Hazard Rate Kernel Estimator UnderTruncated and Censored Data.Communications in Statistics-Theory and Methods, 36, Issue 1, 155-173.
  20. Lo, S.H. Mack, Y.P. and Wang, J.L. (1989). Density and Hazard Rate Estimation for Censored Data via Strong Representation of Kaplan-Meier Estimator. Probability Theory and Related Fields,80, 461-472.
  21. Masry, E. (2005). Nonparametric Regression Estimation for Dependent Functional Data: Asymptotic Normality. Stochastic Processes and Application,115,155-177.
  22. Nassiri, A. Delcroix, M. and Bonneu, M. (2000). Estimation non Parametrique du Taux de Hasard: Application a des Durées de Chômage Censurées à Droite. Annales d’économie et de Statistique, 58,215232.
  23. Nielsen, J.P. (1998). Marker Dependent Kernel Estimation from Local Linear Estimation. Scandinavian Actuarial Journal, 2, 113-224.
  24. Padgett, W.J. and Mc Nichols, D.T.(1984). Nonparametric Density Estimation from Censored Data. Communications in Statistics, Theory, and Methods, 13, 1581-1611.
  25. Prakasa Rao B.L.S. (2012). Associated Sequences, Demi Martingales and Nonparametric Inferences. Probability and its Applications, Springer Basel AG.
  26. Roussas, GG. (1991). Kernel Estimates Under Association: Strong Uniform Consistency. Statistics and Probability Letters, 12, 393-403.
  27. Roussas, GG. (2000). Asymptotic Normality of the Kernel Estimate of a Probability Density Function under Association. Statistics and Probability Letters, 50,1-12.
  28. Silverman, B. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman&Hall.
  29. Spierdijk, L. (2008). Nonparametric Conditional Hazard Rate Estimation: a Local Linear Approach. Computational Statistics and Data Analysis, 52, 2419-2434.
  30. Tanner, M.A. and Wong, W.H. (1983). The Estimation of the Hazard Function from Randomly Censored Data by Kernel Methods. Annals of Statistics, 11, 989-993.
  31. Van Keilegom, I. and Veraverbeke, N. (2001). Hazard Rate Estimation in Nonparametric Regression with Censored Data. Annals of the Institute of Statistical Mathematics, 53, 730-745.
  32. Ying, Z. and Wei, L.J. (1994). The Kaplan-Meier Estimate for Dependent Failure Time Observations. Journal Multivariate Analysis, 50,17-29.