A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
-
Salah Khardani
and
Abdelkader Benkhaled
Abstract
In this paper, we investigate the problem of the local linear estimation of the conditional ageing intensity function, when the variable of interest is subject to random right-censored. We establish under appropriate conditions the asymptotic normality of this estimator.
Acknowledgement
Authors greatly thank the Editor in chief, the Associate Editor and the anonymous referees for a careful reading of the paper and for their valuable comments and suggestions which improved the quality of this paper substantially.
(Communicated by Gejza Wimmer )
References
[1] Bhattacharjee, S.—Nanda, A. K.—Misra, S. K.: Reliability analysis using ageing intensity function, Stat. Probab. Lett. 83(5) (2013), 1364–1371.10.1016/j.spl.2013.01.016Search in Google Scholar
[2] Bosq, D.: Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, 2nd edition, New-York, Springer Verlag, 1999.Search in Google Scholar
[3] Bryson, M. C.—Siddiqui, M.: Some criteria for ageing, J. Amer. Statist. Assoc. 64 (1969), 1472–1483.10.1080/01621459.1969.10501072Search in Google Scholar
[4] Bradley, R.: Introduction to Strong Mixing Conditions, Volumes 1–3, Kendrick Press, 2007.Search in Google Scholar
[5] Cai, Z.: Estimating a distribution function for censored time series data, J. Multivariate Anal. 78 (2001), 299–318.10.1006/jmva.2000.1953Search in Google Scholar
[6] Cai, Z.: Asymptotic properties of Kaplan-Meier estimator for censored dependent data Statist. Probab. Lett. 37 (1998), 381–389.10.1016/S0167-7152(97)00141-7Search in Google Scholar
[7] Dedecker, J.—Doukhan, P.—Lang, G.—Leon, J. R.—Louhichi, S.—Prieur, C.: Weak Dependence with Examples and Applications. Lecture Notes in Statist. 190, Springer-Verlag, 2007.10.1007/978-0-387-69952-3Search in Google Scholar
[8] Doukhan, P.: Mixing, Properties and Examples}. Lectures Notes in Statist. 85, Springer Verlag, New-York, 1994.10.1007/978-1-4612-2642-0_3Search in Google Scholar
[9] Fan, J.—Yao, Q.—Tong, H.: Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems, J. Biometrika 83 (1996), 189–206.10.1093/biomet/83.1.189Search in Google Scholar
[10] Fan, J.—Yao, Q.: Nonlinear Time Series: Nonparametric and Parametric Methods, Springer, Berlin, 2003.10.1007/978-0-387-69395-8Search in Google Scholar
[11] Jiang, R.—Ji, P.—Xiao, X.: Ageing property of unimodal failure rate models, Rel. Eng. Syst. Safety 79 (2003), 113–116.10.1016/S0951-8320(02)00175-8Search in Google Scholar
[12] Kaplan, E. L.—Meier, P.: Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481.10.1007/978-1-4612-4380-9_25Search in Google Scholar
[13] Khardani, S.—Semmar, S.: Nonparametric conditional density estimation for censored data based on a recursive kernel, Electron. J. Stat. 8(2) (2014), 2541–2556.10.1214/14-EJS960Search in Google Scholar
[14] Khardani, S.—Lemdani, M.—Ould Saïd, E.: Some asymptotic properties for a smooth kernel estimator of the conditional mode under random censorship, J. Korean Statist. Soc. 39 (2010), 455–469.10.1016/j.jkss.2009.10.001Search in Google Scholar
[15] Khardani, S.—Lemdani, M.—Ould Saïd, E.: Uniform rate of strong consistency for a smooth kernel estimator of the conditional mode for censored time series, J. Statist. Plann. Inference 141 (2011), 3426–3436.10.1016/j.jspi.2011.04.023Search in Google Scholar
[16] Lai, C. D.—Xie, M.: Stochastic Ageing and Dependence for Reliability, Springer-Verlag, New York, 2006.Search in Google Scholar
[17] Misra, S. K.—Bhattacharjee, S.: A case study of ageing intensity function on censored data, Alexandria Engineering J. 57 (2018), 3931–3952.10.1016/j.aej.2018.03.009Search in Google Scholar
[18] Nanda, A.—Bhattacharjee, S.—Alam, S.: Properties of ageing intensity function, Stat. Probab. Lett. 77 (2007), 365–373.10.1016/j.spl.2006.08.002Search in Google Scholar
[19] Spierdijk, L.: Nonparametric conditional hazard rate estimation: A local linear approach, Comput. Statist. Data Anal. 52(5) (2008), 2419–2434.10.1016/j.csda.2007.08.007Search in Google Scholar
[20] Sunoj, S.—Rasin, R.: A quantile-based study on ageing intensity function, Comm. Statist. Theory Methods 47 (2017), 5474–5484.10.1080/03610926.2017.1395049Search in Google Scholar
[21] Szymkowiak, M.: Generalized ageing intensity functions, Rel. Eng. Syst. Safety 178 (2018), 198–208.10.1016/j.ress.2018.06.012Search in Google Scholar
[22] Xiong, X.—Ou, M.: Non parametric estimation of the conditional density function with right-censored and dependent data, Comm. Statist. Theory Methods, https://doi.org/10.1080/03610926.2019.1691230.10.1080/03610926.2019.1691230Search in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
