分位数回归及其在糖尿病治疗中的应用-概率论与数理统计专业论文.docx

ABSTRACT Generally we take advantage of regression analysis to study relationship between one random variable and one or more controllable variabl倒 when we model to survival data. For censored data，we common use Cox proportional hazard model which is fiexible and received many attentions. However ，this ‘ model places signi自cant 创sumptions on the behavior of conditional survival functions and sometimes theωsumptions is unfounded. Censored quantile regression proposed this paper is a more fiexible alternative approach than Cox proportional hazard model. Especially，the regression quantile coefficients are interpretable 困 direct regression effects on the survival times. It may estimate the quantile function of the conditional distribution and reprωent the conditional distribution with the different quantile estimate function in the different position ，thus we can obtain the more information about the conditional distribution. Censored quantile regression can be viewed as generalizations to the quantile regression ，so the paper fi.rstly introduce the theory of quanti1e regr创sion including the calculation about quantile regression and properties and the the asymptotic of quantile regression estimators. Secondly，the theory of survival analysis is described ，ínvolving to theory of Cox regr四sion in survival data and details of censored quantile regression. At 1ωt we apply censored quantile regr倒sion to censored data of diabetes and obtain different 1\ regr创sion functions in different quantile point of survival time which give ? some prevention and treatment proposals for diabetωpatients. KEY WORDS: quantile regr倒sion ; survival 阻alysis ; censoríng ; Cox regr倒sion ; diabetes 目录 第…章绪论 1 1.1 分位数回归理论的演进 1 1.2 论文的主要内容 3 第工章分位数回归模型 4 2.1 分位数的基本概念 4 2.1.1分位数和最优化 4 ‘ 2.1.2 分位数回归的计算 6 2.1.3 分位数的代数性质 7 2.1.4 解释分位数回归模型 8 2.2 分位数回归的估计及渐近性质 9 2.3 分位数凹归估计最的检验 13 第三章生存分析基本理论， .四 3.1 删失 15 3.2 生存分析的基本函数 16 3.3 生存分析的基本方法 19 3.4