| Survival analysis has become one of the most important areas in biostatistics,and is widely used in medicine,actuarial science,economics and other fields.Left-truncated data and right-censored data are two types of the incomplete data,which often occur in survival analysis.This dissertation mainly studies the conditional distribution function with dependent and left-truncated data,and the conditional hazard function under right-censored data.The structure of this dissertation is arranged as follows.In the first chapter,we introduce the background and current researches for left-truncated and right-censored data.In the chapter 2,based on the idea of local polynomial double-smoother,we propose local polynomial double-smoothing estimator of a conditional distribution function with dependent and left-truncated data.Asymptotic normality of the estimator is established.The results of simulation show that in each case,the local linear estimator performs better than the local constant estimator,and the double-smoothing estimator performs better than the single-smoothing estimator.In the chapter 3,we construct a re-weighted Nadaraya-Watson estimator of conditional hazard function under right-censored data,which is based on the idea of re-weighted Nadaraya-Watson estimator,and asymptotic normality of the estimator is established.The simulation results show that the mean squared errors of the proposed estimation is the same as the local linear estimation,and both are smaller than the local constant estimation.The last chapter summaries the dissertation. |
