Simulating the behavior of a kernel M-estimator for left-truncated and associated model

References

• Adjoudj, L., and A. Tatachak. 2019. Conditional quantile estimation for truncated and associated data. Communications in Statistics - Theory and Methods 48 (18):4598–641. doi:10.1080/03610926.2018.1498895.
   Web of Science ®Google Scholar
• Boente, G., and R. Fraiman. 1989. Robust nonparametric regression estimation for dependent observations. The Annals of Statistics 17:1242–56.
   Web of Science ®Google Scholar
• Boente, G., and R. Fraiman. 1990. Asymptotic distribution of robust estimators for nonparametric models from mixing processes. The Annals of Statistics 18:891–906.
   Web of Science ®Google Scholar
• Bulinski, A. V. 1996. On the convergence rates in the central limit theorem for positively and negatively dependent random fields, In: Ibragimov, I. A. and Zaitsev, A. Yu. (eds.), Probab. Theory and Math. Statist., Gordon and Breach, pp. 3–14.
   Google Scholar
• Bulinski, A., and A. Shashkin. 2007. Limit theorems for associated random fields and related systems. Vol. 10. Advanced series on statistical science & applied probability. Ole E. Barndorff-Nielsen ed., World Scientific.
   Google Scholar
• Chaubey, Y. P., I. Dewan, and J. Li. 2011. Smooth estimation of survival and density functions for a stationary associated process using Poisson weights. Statistics & Probability Letters 81 (2):267–576. doi:10.1016/j.spl.2010.10.010.
   Web of Science ®Google Scholar
• Chen, J., and L. Zhang. 2009. Asymptotic properties of nonparametric M-estimation for mixing functional data. Journal of Statistical Planning and Inference 139 (2):533–46. doi:10.1016/j.jspi.2008.05.007.
   Web of Science ®Google Scholar
• Chen, J., M. T. Chao, and S. H. Lo. 1995. On strong uniform consistency of the Lynden-Bell estimator for truncation data. The Annals of Statistics 23:440–9.
   Web of Science ®Google Scholar
• Collomb, G., and W. Härdle. 1986. Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations. Stochastic Processes and Their Applications 23 (1):77–89. doi:10.1016/0304-4149(86)90017-7.
   Web of Science ®Google Scholar
• Derrar, S., A. Laksaci, and E. Ould Saïd. 2015. On the nonparametric estimation of the functional ψ-regression for a random left-truncation model. Journal of Statistical Theory and Practice 9 (4):823–49. doi:10.1080/15598608.2015.1032455.
   Web of Science ®Google Scholar
• Derrar, S., A. Laksaci, and E. Ould Saïd. 2020. M-estimation of the regression function under random left truncation and functional time series model. Statistical Papers 61 (3):1181–202. doi:10.1007/s00362-018-0979-z.
   Web of Science ®Google Scholar
• Douge, L. 2007. Vitesses de convergence dans la loi forte des grands nombres et dans l’estimation de la densité pour des variables alé atoires associées. Comptes Rendus de l'Académie des Sciences - Series I 344 (8):515–8. doi:10.1016/j.crma.2007.02.017.
   Google Scholar
• Doukhan, P., and M. Neumann. 2007. Probability and moment inequalities for sums of weakly dependent random variables, with applications. Stochastic Processes and Their Applications 117 (7):878–903. doi:10.1016/j.spa.2006.10.011.
   Web of Science ®Google Scholar
• Esary, J., F. Proschan, and D. Walkup. 1967. Association of random variables with applications. The Annals of Mathematical Statistics 38 (5):1466–76. doi:10.1214/aoms/1177698701.
   Google Scholar
• Guessoum, Z., E. Ould Saïd, O. Sadki, and A. Tatachak. 2012. A note on the Lynden-Bell estimator under association. Statistics & Probability Letters 82 (11):1994–2000. doi:10.1016/j.spl.2012.06.016.
   Web of Science ®Google Scholar
• Hampel, F. R., E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel. 1986. Robust statistics: The approach based on influence functions. Wiley series in probability and mathematical statistics.
   Google Scholar
• Härdle, W. 1984. Robust regression function estimation. Journal of Multivariate Analysis 14 (2):169–80. doi:10.1016/0047-259X(84)90003-4.
   Web of Science ®Google Scholar
• Härdle, W. 1989. Asymptotic maximal derivation of M-smoothers. Journal of Multivariate Analysis 29 (2):163–79. doi:10.1016/0047-259X(89)90022-5.
   Web of Science ®Google Scholar
• Härdle, W., and S. Luckhaus. 1984. Uniform consistency of a class of regression estimators. The Annals of Statistics 12:612–23.
   Web of Science ®Google Scholar
• Huber, P. J. 1964. Robust estimation of a location parameter. The Annals of Mathematical Statistics 35 (1):73–101. doi:10.1214/aoms/1177703732.
   Google Scholar
• Huber, P. J. 1981. Robust statistics. New York: Wiley.
   Google Scholar
• Jin, Z. 2007. M-estimation in regression modes for censored data. Journal of Statistical Planning and Inference 137 (12):3894–903. doi:10.1016/j.jspi.2007.04.008.
   Web of Science ®Google Scholar
• Kim, T.-S. 1988. A central limit theorem for associated random vectors. Communications of the Korean Mathematical Society 3 (1):25–35.
   Google Scholar
• Lemdani, M., and E. Ould Saïd. 2017. Nonparametric robust regression estimation for censored data. Statistical Papers 58 (2):505–25. doi:10.1007/s00362-015-0709-8.
   Web of Science ®Google Scholar
• Liebscher, E. 2001. Estimation of the density and the regression function under mixing conditions. Statistics & Decisions 19 (1):9–26.
   Google Scholar
• Lynden-Bell, D. 1971. A method of allowing for known observational selection in small samples applied to 3CR quasars. Monthly Notices of the Royal Astronomical Society 155 (1):95–118. doi:10.1093/mnras/155.1.95.
   Web of Science ®Google Scholar
• Maronna R. A, Martin R. D., Yohai V. J., and M. Salibián-Barrera. 2019. Robust statistics: Theory and methods (with R). Wiley series in probability and statistics. 2nd ed.
   Google Scholar
• Masry, E. 1986. Recursive probability density estimation for weakly dependent processes. IEEE Transactions on Information Theory 32 (2):254–67. doi:10.1109/TIT.1986.1057163.
   Web of Science ®Google Scholar
• Oliveira, P. E. 2012. Asymptotics for associated random variables. Berlin, Heidelberg: Springer Verlag.
   Google Scholar
• Ould Saïd, E., and M. Lemdani. 2006. Asymptotic properties of a nonparametric regression function estimator with randomly truncated data. Annals of the Institute of Statistical Mathematics 58 (2):357–78. doi:10.1007/s10463-005-0011-y.
   Web of Science ®Google Scholar
• Prakasa Rao, B. L. S. 2012. Associated sequences, demimartingales and nonparametric inference. Probability and its applications. Birkhäuser: Springer.
   Google Scholar
• Ren, J. J., and M. Gu. 1997. Regression M-estimators with doubly censored data. The Annals of Statistics 25:2638–64.
   Web of Science ®Google Scholar
• Serfling, R. J. 1980. Approximation theorems of mathematical statistics. New York: Wiley.
   Google Scholar
• Wang, J. F., and H. Y. Liang. 2012. Asymptotic properties for an M-estimator of the regression function with truncation and dependent data. Journal of the Korean Statistical Society 41 (3):351–67. doi:10.1016/j.jkss.2011.12.001.
   Web of Science ®Google Scholar
• Woodroofe, M. 1985. Estimating a distribution function with truncated data. The Annals of Statistics 13:163–77.
   Web of Science ®Google Scholar