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CLT for single functional index quantile regression under dependence structure

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[1] A. Aït Saidi, F. Ferraty and R. Kassa, Single functional index model for a time series, Revue Roumaine de Mathématique Pures Appliquées, 50 (2002), 321–330. Search in Google Scholar

[2] A. Aït Saidi, F. Ferraty, R. Kassa and P. Vieu, Cross-validated estimation in the single functional index model, Statistics, 42(6) (2008), 475–494.10.1080/02331880801980377 Search in Google Scholar

[3] S. Attaouti, A. Laksaci and E. Ould-Saïd, A note on the conditional density estimate in the single functional index model, Statistics and Probability Letters, 81(1) (2011), 45–53.10.1016/j.spl.2010.09.017 Search in Google Scholar

[4] S. Attaoui, On the Nonparametric Conditional Density and Mode Estimates in the Single Functional Index Model with Strongly Mixing Data, Sankhyã: The Indian Journal of Statistics, 76(A) (2014), 356–378.10.1007/s13171-014-0051-6 Search in Google Scholar

[5] S. Attaoui and N. Ling, Asymptotic Results of a Nonparametric Conditional Cumulative Distribution Estimator in the single functional index Modeling for Time Series Data with Applications, Metrika, 79 (2016), 485–511.10.1007/s00184-015-0564-6 Search in Google Scholar

[6] Z. Cai, Estimating a distribution function for censored time series data, J. Multivariate Anal., 78 (2001), 299–318.10.1006/jmva.2000.1953 Search in Google Scholar

[7] Z. Cai, Regression quantiles for time series, Econometric Theory, 18 (2002), 169–192.10.1017/S0266466602181096 Search in Google Scholar

[8] M. Chaouch and S. Khardani, Randomly Censored Quantile Regression Estimation using Functional Stationary Ergodic Data, Journal of Non-parametric Statistics, 27 (2015), 65–87.10.1080/10485252.2014.982651 Search in Google Scholar

[9] P. Chaudhuri, K. Doksum and A. Samarov, On average derivative quantile regression, Ann. Statist., 25 (1997),715–744.10.1214/aos/1031833670 Search in Google Scholar

[10] J. Dedecker, P. Doukhan, G. Lang, J.R. Leon, S. Louhichi and C. Prieur, Weak Dependence: With Examples and Applications, Lecture Notes in Statistics, 190. New York: Springer-Verlag, 2007. Search in Google Scholar

[11] P. Doukhan, Mixing: Properties and Examples, Lecture Notes in Statistics, 85. New York: Springer-Verlag, 1994. Search in Google Scholar

[12] J. L. Doob, Stochastic Processes, New York: Wiley, 1953. Search in Google Scholar

[13] A. El Ghouch and I. Van Keilegom, Local Linear Quantile Regression with Dependent Censored Data, Statistica Sinica, 19 (2009), 1621–1640. Search in Google Scholar

[14] M. Ezzahrioui and E. Ould-Saïd, Asymptotic results of a nonparametric conditional quantile estimator for functional time series, Comm. Statist. Theory and Methods., 37(16-17) (2008), 2735–2759.10.1080/03610920802001870 Search in Google Scholar

[15] F. Ferraty, A. Rabhi and P. Vieu, Conditional quantiles for functional dependent data with application to the climatic ElNinô phenomenon, Sankhyã B, Special Issue on Quantile Regression and Related Methods, 67(2) (2005), 378–399. Search in Google Scholar

[16] F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis: Theory and Practice, Springer Series in Statistics, Springer, New York, 2006. Search in Google Scholar

[17] A. Gannoun, J. Saracco and K. Yu, Nonparametric prediction by conditional median and quantiles, J. Statist. Plann. Inference., 117 (2003), 207–223.10.1016/S0378-3758(02)00384-1 Search in Google Scholar

[18] N. Kadiri, A. Rabhi and A. Bouchentouf, Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship, Journal Dependence Modeling, 6(1) (2018), 197–227.10.1515/demo-2018-0013 Search in Google Scholar

[19] E. Kaplan and P. Meier, Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association, 53 (1958), 457–481.10.1080/01621459.1958.10501452 Search in Google Scholar

[20] J-P. Lecoutre and E. Ould-Saïd, Hazard rate estimation for strong mixing and censored processes, J. Nonparametr. Stat. 5 (1995), 83–89.10.1080/10485259508832636 Search in Google Scholar

[21] H.Y. Liang and J. Ua-lvarez, Asymptotic Properties of Conditional Quantile Estimator for Censored Dependent Observations, Annals of the Institute of Statistical Mathematics, 63 (2011), 267–289.10.1007/s10463-009-0230-8 Search in Google Scholar

[22] Z. Lin and C. Lu, Limit theory of mixing dependent random variables, Mathematics and its applications, Sciences Press, Kluwer Academic Publishers, Beijing, 1996. Search in Google Scholar

[23] N. Ling and Q. Xu, Asymptotic normality of conditional density estimation in the single index model for functional time series data, Statistics and Probability Letters, 82 (2012), 2235–2243.10.1016/j.spl.2012.08.018 Search in Google Scholar

[24] N. Ling, Z. Li and W. Yang, Conditional density estimation in the single functional index model for α -mixing functional data, Communications in Statistics: Theory and Methods, 43(3) (2014), 441–454.10.1080/03610926.2012.664236 Search in Google Scholar

[25] E. Masry and D. Tøjstheim, Nonparametric estimation and identification of nonlinear time series, Econometric Theor., 11 (1995), 258–289.10.1017/S0266466600009166 Search in Google Scholar

[26] E. Masry, Nonparametric Regression Estimation for Dependent Functional Data: Asymptotic Normality, Stochastic Processes and their Applications, 115 (2005), 155–177.10.1016/j.spa.2004.07.006 Search in Google Scholar

[27] C. Muharisa, F. Yanuar and D. Devianto, Simulation Study The Using of Bayesian Quantile Regression in Non-normal Error, Cauchy: Jurnal Matematika Murni dan Aplikasi, 5(3) (2018), 121–126.10.18860/ca.v5i3.5633 Search in Google Scholar

[28] E. Ould-Saïd, A Strong Uniform Convergence Rate of Kernel Conditional Quantile Estimator under Random Censorship, Statistics and Probability Letters, 76 (2006), 579–586.10.1016/j.spl.2005.09.002 Search in Google Scholar

[29] W-J. Padgett, Nonparametric Estimation Of Density And Hazard Rate Functions When Samples Are Censored, In P.R. Krishnaiah and C.R. Rao (Eds). Handbook of Statist. 7, pp. 313–331. Elsevier/North-Holland. Amsterdam. Science Publishers, 1988.10.1016/S0169-7161(88)07018-X Search in Google Scholar

[30] G. Roussas, Nonparametric estimation of the transition distribution function of a Markov process, Ann. Statist., 40 (1969), 1386–1400.10.1214/aoms/1177697510 Search in Google Scholar

[31] M. Samanta, Nonparametric estimation of conditional quantiles, Statist. Probab. Lett., 7 (1989), 407–412.10.1016/0167-7152(89)90095-3 Search in Google Scholar

[32] S. Sarmada and F. Yanuar, Quantile Regression Approach to Model Censored Data, Science and Technology Indonesia, 5(3) (2020), 79–84.10.26554/sti.2020.5.3.79-84 Search in Google Scholar

[33] M. Tanner and W-H. Wong, The estimation of the hazard function from randomly censored data by the kernel methods, Ann. Statist., 11 (1983), 989–993. Search in Google Scholar

[34] I. Van-Keilegom and N. Veraverbeke, Hazard rate estimation in nonpara-metric regression with censored data, Ann. Inst. Statist. Math., 53 (2001), 730–745.10.1023/A:1014696717644 Search in Google Scholar

[35] H. Wang and Y. Zhao, A kernel estimator for conditional t-quantiles for mixing samples and its strong uniform convergence, (in chinese), Math. Appl. (Wuhan)., 12 (1999), 123–127. Search in Google Scholar

[36] F. Yanuar, H. Laila and D. Devianto, The Simulation Study to Test the Performance of Quantile Regression Method With Heteroscedastic Error Variance, Cauchy: Jurnal Matematika Murni dan Aplikasi, 5(1) (2017), 36–41.10.18860/ca.v5i1.4209 Search in Google Scholar

[37] F. Yanuar, H. Yozza, F. Firdawati, I. Rahmi, and A. Zetra, Applying Bootstrap Quantile Regression for The Construction of a Low Birth Weight Model, Makara Journal of Health Research, 23(2) (2019), 90–95.10.7454/msk.v23i2.9886 Search in Google Scholar

[38] Y. Zhou and H. Liang, Asymptotic properties for L1 norm kernel estimator of conditional median under dependence, J. Nonparametr. Stat., 15 (2003), 205–219.10.1080/1048525031000089293 Search in Google Scholar

eISSN:
2066-7752
Lingua:
Inglese
Frequenza di pubblicazione:
2 volte all'anno
Argomenti della rivista:
Mathematics, General Mathematics