比例风险模型下参数估计的两种MM算法的一些应用

对于带有删失机制的生存数据的研究,比例风险模型是应用最为广泛的统计模型之一。实际中,为得到其参数的极大似然估计需要采用数值方法计算得分方程的解。MinorizationMaximization算法(以下简称"MM算法")将求解复杂的目标函数的极值问题转化为求解简单的代理函数的极值问题。本文主要探讨,在比例风险模型下通过两种不同的思想为偏似然函数构造代理函数,从而得到的两种MM算法。通过数值模拟和实际数据分析实现这两种MM算法在比例风险模型下的一些应用。     

Assessing the default risk by means of a discrete‐time survival analysis approach

In this paper, the problem of company distress is assessed by means of a multi‐period model that exploits the potentialities of the survival analysis approach when both survival times and regressors are measured at discrete points in time. The discrete‐time hazards model can be used both as an empirical framework in the analysis of the causes of the deterioration process that leads to the default and as a tool for the prediction of the same event. Our results show that the prediction accuracy of the duration model is better than that provided by a single‐period logistic model. It is also shown that the predictive power of the discrete‐time survival analysis is enhanced when it is extended to allow for unobserved individual heterogeneity (frailty). Copyright © 2008 John Wiley & Sons, Ltd.     

Maximum likelihood inference for the Cox regression model with applications to missing covariates

In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model [D.R. Cox, Regression models and life tables (with discussion), Journal of the Royal Statistical Society, Series B 34 (1972) 187–220; D.R. Cox, Partial likelihood, Biometrika 62 (1975) 269–276] both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.     

临汾地面沉降数值模拟及其与地裂缝灾害关系研究

临汾市区是继西安、大同等地区之后又一地裂缝灾害比较严重的地区, 已经严重影响着临汾市经济的可持续性发展。经研究表明, 地下水超采为影响该区地裂缝灾害的第二大因子, 它是通过地面沉降来促使地裂缝的形成和发展。本文通过对临汾市区地面沉降进行数值模拟, 总结出了地面沉降的变化规律。分析认为, 地裂缝灾害的易出现部位为沉降梯度陡变带, 即沉降梯度最大处。