81
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

On the Nonparametric Estimation of the Functional ψ-Regression for a Random Left-Truncation Model

, &
Pages 823-849 | Received 10 Jul 2014, Accepted 18 Mar 2015, Published online: 28 May 2015

References

  • Andersen, P. K., O. Borgan, R. D. Gill, and N. Keiding. 1993. Statistical models based on counting processes. New York, NY: Springer.
  • Attouch, M., A. Laksaci, and E. Ould Saïd. 2009. Asymptotic distribution of robust estimator in nonparametric functional models, Comm. Stat. Theory Methods, 38, 1317–1335.
  • Attouch, M., A. Laksaci, and E. Ould Saïd. 2010. Asymptotic normality of a robust estimator of the regression function for functional time series. J. Korean Stat. Soc., 39, 489–500.
  • Attouch, M., A. Laksaci, and E. Ould Saïd. 2012. Robust regression for functional time series data. J. Jpn. Stat. Soc., 42, 125–143.
  • Azzedine, N., A. Laksaci, and E. Ould Saïd. 2008. On the robust nonparametric regression estimation for functional regressor. Stat. Prob. Lett., 78, 3216–3221.
  • Boente, G., and R. Fraiman. 1989. Nonparametric regression estimation. J. Multivariate Anal., 29, 180–198.
  • Boente, G., and R. Fraiman. 1990. Asymptotic distribution of robust estimators for nonparametric models from mixing processes. Ann. Stat., 18, 891–906.
  • Boente, G., and D. Rodriguez. 2006. Robust estimators of high order derivatives of regression function. Stat. Probabil. Lett., 76, 1335–1344.
  • Boente, G., W. Gonzalez-Manteiga, and A. Pérez-Gonzalez. 2009. Robust nonparametric estimation with missing data. J. Stat. Plan. Inference, 139, 571–592.
  • Chen, J., and L. Zhang. 2009. Asymptotic properties of nonparametric M-estimation for mixing functional data, J. Stat. Plan. Inference, 139, 533–546.
  • Collomb, G., and W. Härdle. 1986. Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations. Stoch. Proc. Appl., 23, 77–89.
  • Crambes, C., L. Delsol, and A. Laksaci. 2008. Robust nonparametric estimation for functional data, J. Nonparametric Stat., 20, 573–598.
  • Ferraty, F., and Y. Romain. 2011. The Oxford handbook of functional data analysis. New York, NY: Oxford University Press.
  • Ferraty, F., and P. Vieu. 2006. Nonparametric functional data analysis. Theory and practice. New York, NY: Springer-Verlag.
  • Gheriballah, A., A. Laksaci, and S. Sekkal. 2013. Nonparametric M-regression for functional ergodic data. Stat. Prob. Lett., 83, 902–908.
  • He, S., and G. Yang. 1994. Estimating a lifetime distribution under different sampling plan. In Statistical decision theory and related topics, ed. S. S. Gupta and J. O. Berger, Vol. 5, 73–85. New York: Springer.
  • He, S., and G. Yang. 1998. Estimation of the truncation probability in the random truncation model. Ann. Stat., 26, 1011–1027.
  • Horrigue, W., and E. Ould Saïd. 2011. Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors. Random Oper. Stoch. Equations, 19, 131–156.
  • Horrigue, W., and E. Ould Saïd. 2014. Nonparametric regression quantile estimation for dependant functional data under random censorship: Asymptotic normality. Commun. Stat. Theory Methods. doi: 10.1080/03610926.2013.784993.
  • Huber, P. J. 1964. Robust estimation of a location parameter. Ann. Math. Stat., 35, 73–101.
  • Laïb, N., and E. Ould Saïd. 2000. A robust nonparametric estimation of the autoregression function under an ergodic hypothesis. Can. J. Stat., 28, 817–828.
  • Lemdani, M., and E. Ould Saïd. 2007. Asymptotic behavior of hazard rate kernel estmator under truncated and censored data, Commun. Stat. Theory Methods, 37, 155–173.
  • Loève, M. 1997. Probability theory I. New-York, NY: Springer-Verlag.
  • Lynden-Bell, D. 1971. A method of allowing for known observational selection in small samples applied to 3CR quasars. Monthly Notices R. Astronom. Soc., 155, 95–118.
  • Ould Saïd, E., and M. Lemdani. 2006. Asymptotic properties of a nonparametric regression function estimator with randomly truncated data. Ann. Inst. Stat. Math., 58, 357–378.
  • Stone, C. 1981. Optimal rates of convergence for nonparametric regression. Ann. Stat., 9, 1348–1360.
  • Stute, W. 1993. Almost sure representations of the product-limit estimator for truncated data. Ann. Stat., 21, 146–156.
  • Wang, J., H. Y. Liang, and G. Fan, 2012a. Asymptotic properties for an M-estimator of the regression function with truncation and dependent data. J. Korean Stat. Soc., 41, 35–367.
  • Wang, J., H. Y. Liang, and G. Fan. 2012b. Local M-estimation of nonparametric regression with left-truncated and dependent data. Sci. Sin. Math., 42, 995–1015.
  • Woodroofe, M. 1985. Estimating a distribution function with truncated data. Ann. Stat., 13, 163–177.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.