Nonparametric Maximum Likelihood Estimation in the Correlated Gamma-Frailty Model with Current Status Family Data

• Main Authors: Wen Chi-Chung, 溫啟仲
• Other Authors: Chang I-shou
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/23526878915749507175

博士 === 國立中央大學 === 數學研究所 === 89 === The nonparametric maximum likelihood estimate (NPMLE) for the parameters in the correlated gamma-frailty model with current status family data is studied. The identifiability of the parameters and the existence of NPMLE are established under certainregularity conditions. In addition to the asymptotic consistency, the asymptotic normality and efficiency of the NPMLE for the regression coefficient and frailty parameters are proved, and a convergence rate of the NPMLE for the baseline cumulative hazard function is established. The profile likelihood ratio statistic for hypothesis testing and the related confidence regions for the regression coefficient and frailty parameters are also studied.