纵向数据下非参半参回归模型的局部估计及其应用
发布时间：2018-08-03 20:06
【摘要】：纵向数据是一类重要的数据类型,它在社会学、经济学、生物医学、传染病学以及其它的自然科学领域有着广泛的应用。回归模型常用来研究协变量与响应变量间的相关关系。特别是,近年来非参和半参回归模型由于其灵活多变的特点以及能够挖掘实际问题中响应变量和相关协变量间潜在关系的能力而受到广泛的关注和研究。基于此,本文对纵向数据下非参半参回归模型的局部估计问题展开了若干研究,主要工作如下：(1)针对灵活多变且在纵向数据分析中非常有用的变系数模型,我们在第二章中讨论了它的估计问题。基于乔里斯基分解和剖面最小二乘估计方法,加入个体内的相关性构造了一个新的可以同时估计回归函数和协方差结构的估计方法。进一步建立了所得估计的大样本性质。大量的数值模拟分析和实例应用都验证了所提估计方法的有效性。(2)为了克服纵向数据中多元协变量的维数祸根问题,我们在第三章研究了具有降维功效的纵向数据单指标模型的估计问题。基于乔里斯基分解和局部线性估计方法构造了一个新的有效的估计过程来得到纵向数据单指标模型中的非参和参数部分的估计,并建立了它们的渐近正态性。数值模拟和实例分析都证实了所提估计方法的稳定性和优良性。(3)血管通路对于肾透析的病人至关重要,已有的医学研究表明血管通路CVC常会引发感染且对透析后的血液含量有不好的影响,而转换为血管通路AVF对病人有很好的治疗效果。我们感兴趣的转换血管通路的动态影响以及是否与转换时间有关等问题还没有相应的统计研究,进一步此类纵向数据分析需要包含多个时间指标变量。针对这一系列的问题,在第四章我们构造了一个一般化的灵活的模型,它能同时刻画处理方式转换的动态影响、相关协变量的动态影响以及随着处理方式时间、日历时间和转换时间的变化趋势,且关心的转换影响依赖于转换时间和转换后的时间。基于局部线性估计和回切的估计过程,得到了模型中所有未知函数的估计。同时也研究了所得到的估计的大样本性质。数值模拟验证了所提方法的良好的有限样本表现。最后将所提的模型和估计方法应用到了探究透析病人转换血管通路对其血液中白蛋白(albumin)的动态影响。统计分析结果显示透析病人血管通路从CVC转换为AVF能够提高其血液中白蛋白(albumin)的含量且越早转换越好。(4)由血管通路引发的并发症是导致肾透析病人高的住院率和死亡率的主要原因之一,从而也导致了高额的医疗费用。因此,在第四章的基础上,我们在第五章研究透析病人转换血管通路对其住院情况的动态影响。针对这一问题,我们构造了一个一般化的灵活的处理方式转换影响的广义模型。基于局部拟似然和局部线性估计方法,得到了模型中所有未知函数的非参估计,同时给出了它们的大样本性质。数值模拟和实例数据分析进一步验证了所提方法的有效性。详尽的统计分析结果显示透析病人血管通路从CVC转换为AVF能有效地降低其住院率,且与转换时间有关。我们的方法同样适用于其它的处理方式改变的问题研究。本文的结论和方法丰富了纵向数据下非参半参回归模型的估计方法,将有助于分析在经济学、生物统计等应用领域中遇到的复杂多变的问题。
[Abstract]:Vertical data is an important type of data type, which is widely used in sociology, economics, biomedicine, infectious diseases and other natural sciences. The regression model is often used to study the correlation between covariate and response variables. In particular, the non parametric and semi parametric regression models have been characterized by its flexible and changeable characteristics in recent years. As well as the ability to excavate the potential relationship between the response variables and the associated covariate in the actual problems, it has received extensive attention and research. Based on this, this paper has carried out a number of studies on the local estimation problem of the non ginseng regression model under the longitudinal data. The main work is as follows: (1) the needle is flexible and in the longitudinal data analysis very well. With the variable coefficient model, we discuss its estimation in the second chapter. Based on the Jo Riski decomposition and the section least square estimation, a new estimation method for the simultaneous estimation of the regression function and covariance structure is constructed by adding the correlation in the body. The large sample properties of the estimated results are further established. Numerical simulation analysis and example application verify the effectiveness of the proposed method. (2) in order to overcome the dimensionality of the multivariate covariate in the longitudinal data, we study the estimation of the single index model of the longitudinal data with the function of reducing the dimension in the third chapter. Based on the Joris based decomposition and the local linear estimation method, we construct the one. A new and effective estimation process comes from the estimation of the non parametric and parametric parts in the longitudinal data single index model, and their asymptotic normality is established. Both the numerical simulation and the example analysis confirm the stability and virtuous of the proposed method. (3) the vascular pathway is very important for the patients with renal dialysis, and the medical research table has been established. The vascular pathway CVC often causes infection and has a bad effect on the blood content after dialysis, and the conversion into vascular access AVF has a good therapeutic effect on the patient. We are interested in the dynamic effects of the conversion of vascular access and whether there is no statistical study on the problems related to the conversion time. Further such longitudinal data are further studied. Analysis needs to include multiple time index variables. In this series, we construct a general and flexible model in the fourth chapter, which can simultaneously depict the dynamic effects of the processing mode transformation, the dynamic influence of the associated covariance, the changing trend with the processing time, the calendar time and the conversion time, and the concern. The transformation effect depends on the conversion time and the time after the conversion. The estimation of all the unknown functions in the model is obtained based on the local linear estimation and the estimation of the back cut. The large sample properties of the estimated results are also studied. The numerical simulation shows the good finite sample performance of the proposed method. Finally, the proposed model and the proposed model are presented. The estimation method was applied to explore the dynamic effect of the vascular pathway on the blood albumin (albumin) in the hemodialysis patients. The statistical analysis showed that the change of blood albumin (albumin) in the blood of the dialysis patient from CVC to AVF and the earlier conversion was better. (4) the complications caused by vascular access were renal transmissions. This is one of the main reasons for the high rate of hospitalization and mortality, and thus leads to high medical costs. Therefore, on the basis of the fourth chapter, we study the dynamic effects of dialysis on the patient's hospitalization in the fifth chapter. Based on the local Quasi Likelihood and local linear estimation, the non parametric estimation of all the unknown functions in the model is obtained, and their large sample properties are given. The numerical simulation and case data analysis further verify the effectiveness of the proposed method. The detailed analysis results show that the hemodialysis patients' vascular access is from The conversion of CVC to AVF can effectively reduce the rate of hospitalization and is related to the conversion time. Our method is also applicable to other problems in the process of treatment. The conclusions and methods of this paper enrich the estimation method of non ginseng regression model under the longitudinal data, which will help to analyze the applications in the fields of economics, biological statistics and so on. The complex and changeable problem.
【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.7
[Abstract]:Vertical data is an important type of data type, which is widely used in sociology, economics, biomedicine, infectious diseases and other natural sciences. The regression model is often used to study the correlation between covariate and response variables. In particular, the non parametric and semi parametric regression models have been characterized by its flexible and changeable characteristics in recent years. As well as the ability to excavate the potential relationship between the response variables and the associated covariate in the actual problems, it has received extensive attention and research. Based on this, this paper has carried out a number of studies on the local estimation problem of the non ginseng regression model under the longitudinal data. The main work is as follows: (1) the needle is flexible and in the longitudinal data analysis very well. With the variable coefficient model, we discuss its estimation in the second chapter. Based on the Jo Riski decomposition and the section least square estimation, a new estimation method for the simultaneous estimation of the regression function and covariance structure is constructed by adding the correlation in the body. The large sample properties of the estimated results are further established. Numerical simulation analysis and example application verify the effectiveness of the proposed method. (2) in order to overcome the dimensionality of the multivariate covariate in the longitudinal data, we study the estimation of the single index model of the longitudinal data with the function of reducing the dimension in the third chapter. Based on the Joris based decomposition and the local linear estimation method, we construct the one. A new and effective estimation process comes from the estimation of the non parametric and parametric parts in the longitudinal data single index model, and their asymptotic normality is established. Both the numerical simulation and the example analysis confirm the stability and virtuous of the proposed method. (3) the vascular pathway is very important for the patients with renal dialysis, and the medical research table has been established. The vascular pathway CVC often causes infection and has a bad effect on the blood content after dialysis, and the conversion into vascular access AVF has a good therapeutic effect on the patient. We are interested in the dynamic effects of the conversion of vascular access and whether there is no statistical study on the problems related to the conversion time. Further such longitudinal data are further studied. Analysis needs to include multiple time index variables. In this series, we construct a general and flexible model in the fourth chapter, which can simultaneously depict the dynamic effects of the processing mode transformation, the dynamic influence of the associated covariance, the changing trend with the processing time, the calendar time and the conversion time, and the concern. The transformation effect depends on the conversion time and the time after the conversion. The estimation of all the unknown functions in the model is obtained based on the local linear estimation and the estimation of the back cut. The large sample properties of the estimated results are also studied. The numerical simulation shows the good finite sample performance of the proposed method. Finally, the proposed model and the proposed model are presented. The estimation method was applied to explore the dynamic effect of the vascular pathway on the blood albumin (albumin) in the hemodialysis patients. The statistical analysis showed that the change of blood albumin (albumin) in the blood of the dialysis patient from CVC to AVF and the earlier conversion was better. (4) the complications caused by vascular access were renal transmissions. This is one of the main reasons for the high rate of hospitalization and mortality, and thus leads to high medical costs. Therefore, on the basis of the fourth chapter, we study the dynamic effects of dialysis on the patient's hospitalization in the fifth chapter. Based on the local Quasi Likelihood and local linear estimation, the non parametric estimation of all the unknown functions in the model is obtained, and their large sample properties are given. The numerical simulation and case data analysis further verify the effectiveness of the proposed method. The detailed analysis results show that the hemodialysis patients' vascular access is from The conversion of CVC to AVF can effectively reduce the rate of hospitalization and is related to the conversion time. Our method is also applicable to other problems in the process of treatment. The conclusions and methods of this paper enrich the estimation method of non ginseng regression model under the longitudinal data, which will help to analyze the applications in the fields of economics, biological statistics and so on. The complex and changeable problem.
【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.7
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