Then the finite sample performance of the estimator is illustrated on a simulation study.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In survival or reliability studies, it is common to deal with data which are not only incomplete but weakly dependent too.
📊
Key Findings & Data:As main results, we establish a strong uniform consistency rate for the estimator.
💡
Conclusion & Impact:Then the finite sample performance of the estimator is illustrated on a simulation study.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Associated data · Censored data · Convergence rate
Abstract
In survival or reliability studies, it is common to deal with data which are not only incomplete but weakly dependent too. Random right-censoring and random left-truncation are two common forms of such data when they are neither independent nor strongly mixing but rather associated. In this paper, we focus on kernel estimation of the conditional quantile function of a strictly stationary associated random variable $T$ given a $d$-dimensional vector of covariates $X$, under random right-censoring. As main results, we establish a strong uniform consistency rate for the estimator. Then the finite sample performance of the estimator is illustrated on a simulation study.
DJELLADJ, W., TATACHAK, A. (2022). Strong uniform consistency of a kernel conditional quantile estimator for censored and associated data. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 290–311. https://ajindex.com/articles/530526
Abberger, K. Quantile smoothing in financial time series, Statist. Papers 38, 125-148, 1997.
Bhattacharya, P.K. and Gangopadhyay, A. Kernel and nearest neighbour estimation of conditional quantile, Ann. Statist. 18, 1400-1415, 1990.
Bulinski, A. and Shashkin, A. Limit theorems for associated random fields and related systems, Vol 10, Advanced series on statistical science & applied probability, World Scientific, Singapore, 2007.
Cai, Z. Asymptotic properties of Kaplan-Meier estimator for censored dependent data, Statist. Probab. Lett. 37, 381-389, 1998.
Cai, Z. and Roussas, G.G. Kaplan-Meier estimator under association, J. Multivariate Anal. 67, 318-348, 1998.
Chaudhuri, P., Doksum, K. and Samarov, A. On average derivative quantile regression, Ann. Statist. 25, 715-744, 1997.
Dabrowska, D. Nonparametric quantile regression with censored data, Sankhya A 54, 252-259, 1992.
Doukhan, P. Mixing: Properties and Examples, Lect. Notes in Statist. 61, Springer Verlag, 1994.
Doukhan, P. and Louhichi, S. A new weak dependence condition and applications to moment inequalities, Stochastic Process. Appl. 84, 313-342, 1999.
Doukhan, P. and Neumann, M. Probability and moment inequalities for sums of weakly dependent random variables, with applications, Stochastic Process. Appl. 117, 878-903, 2007.
Esary, J., Proschan, F. and Walkup, D. Association of random variables with applications, Ann. Math. Statist. 38, 1466-1476, 1967.
Honda, T. Nonparametric estimation of a conditional quantile for strong mixing processes, Ann. Inst. Statist. Math. 52, 459--470, 2000.
Kaplan, E.M. and Meier, P. Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53, 457-481, 1958.
Koul, H., Susarla, V. and Van Ryzin, J. Regression analysis with randomly right censored data, Ann. Statist. 9, 1276-1288, 1981.
Liang, H.-Y. and de Una-Alvarez, J. Asymptotic properties of conditional quantile estimator for censored dependent observations, Ann. Inst. Statist. Math. 63, 267-289, 2011.
Mehra, K.L., Rao M.S. and Upadrasta S.P. A smooth conditional quantile estimator and related applications of conditional empirical processes, J. Multivariate Anal. 37, 151-179, 1991.
Menni, N. and Tatachak, A. A note on estimating the conditional expectation under censoring and association: strong uniform consistency, Statist. Papers, DOI:10.1007/s00362-016-0801-8, 2016.
Newman, C.M. Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Tong, Y.L