|
|
右删失数据条件密度函数的非参数估计
|
Abstract:
本文考虑响应变量受到随机右删失的回归模型，在右删失数据与未受删失影响数据条件独立的情况下，构造了一种右删失数据条件密度函数的非参数估计量，进而得到该估计量的一致强相合性及其收敛速度，最后通过模拟探究了估计量的估计效果。
In this paper, we consider a regression model in which the response is subject to random right censored. Under the assumption that survival time and censored time are conditional independent, we construct a nonparametric conditional density estimator. The uniform strong consistency of the conditional density estimator and its convergence rate are derived. Finally, we study the accuracy of the estimator.
| [1] | Tj？stheim, D. (1994) Non-Linear Time Series: A Selective Review. Scandinavian Journal of Statistics, 21, 97-130. |
| [2] | Polonik, W. and Yao, Q. (2000) Conditional Minimum Volume Predictive Regions for Stochastic Processes. Journal of the American Statistical Association, 95, 509-519. https://doi.org/10.1080/01621459.2000.10474228 |
| [3] | Hyndman, R.J., Bashtannyk, D.M. and Grunwald, G.K. (1996) Estimating and Visualizing Conditional Densities. Journal of Computational and Graphical Statistics, 5, 315-336. https://doi.org/10.1080/10618600.1996.10474715 |
| [4] | Hyndman, R.J. and Yao, Q. (2002) Nonparametric Estimation and Symmetry Tests for Conditional Density Functions. Journal of Nonparametric Statistics, 14, 259-278. https://doi.org/10.1080/10485250212374 |
| [5] | De Gooijer, J.G. and Zerom, D. (2003) On Conditional Density Estimation. Statistica Neerlandica, 57, 159-176.
https://doi.org/10.1111/1467-9574.00226 |
| [6] | Kaplan, E.L. and Meier, P. (1958) Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53, 457-481. https://doi.org/10.1080/01621459.1958.10501452 |
| [7] | Beran, R. (1981) Nonparametric Regression with Randomly Censored Survival Data. Technical Report, Technical University of California, Berkeley. |
| [8] | Gonzalez-Manteiga W. and Cadarso-Suarez, C. (1994) Asymptotic Properties of a Generalized Kaplan-Meier Estimator with Some Applications. Journal of Nonparametric Statistics, 4, 65-78.
https://doi.org/10.1080/10485259408832601 |
| [9] | Khardani, S. and Semmar, S. (2014) Nonparametric Conditional Density Estimation for Censored Data Based on a Recursive Kernel. Electronic Journal of Statistics, 8, 2541-2556. https://doi.org/10.1214/14-EJS960 |
| [10] | Spierdijk, L. (2008) Nonparametric Conditional Hazard Rate Estimation: A Local Linear Approach. Computational Statistics & Data Analysis, 52, 2419-2434. https://doi.org/10.1016/j.csda.2007.08.007 |
| [11] | Kim, C., Oh, M., Yang, S.J., et al. (2010) A Local Linear Estimation of Conditional Hazard Function in Censored Data. Journal of the Korean Statistical Society, 39, 347-355. https://doi.org/10.1016/j.jkss.2010.03.002 |
| [12] | Hoeffding, W. (1994) Probability Inequalities for Sums of Bounded Random Variables. In: Fisher, N.I. and Sen, P.K., Eds., The Collected Works of Wassily Hoeffding, Springer, New York, NY, 409-426.
https://doi.org/10.1007/978-1-4612-0865-5_26 |
