縱向數(shù)據(jù)下非參半?yún)⒒貧w模型的局部估計(jì)及其應(yīng)用
發(fā)布時(shí)間：2018-08-03 20:06
【摘要】：縱向數(shù)據(jù)是一類重要的數(shù)據(jù)類型,它在社會(huì)學(xué)、經(jīng)濟(jì)學(xué)、生物醫(yī)學(xué)、傳染病學(xué)以及其它的自然科學(xué)領(lǐng)域有著廣泛的應(yīng)用�；貧w模型常用來研究協(xié)變量與響應(yīng)變量間的相關(guān)關(guān)系。特別是,近年來非參和半?yún)⒒貧w模型由于其靈活多變的特點(diǎn)以及能夠挖掘?qū)嶋H問題中響應(yīng)變量和相關(guān)協(xié)變量間潛在關(guān)系的能力而受到廣泛的關(guān)注和研究�；诖�,本文對(duì)縱向數(shù)據(jù)下非參半?yún)⒒貧w模型的局部估計(jì)問題展開了若干研究,主要工作如下：(1)針對(duì)靈活多變且在縱向數(shù)據(jù)分析中非常有用的變系數(shù)模型,我們?cè)诘诙轮杏懻摿怂墓烙?jì)問題�；趩汤锼够纸夂推拭孀钚《斯烙�(jì)方法,加入個(gè)體內(nèi)的相關(guān)性構(gòu)造了一個(gè)新的可以同時(shí)估計(jì)回歸函數(shù)和協(xié)方差結(jié)構(gòu)的估計(jì)方法。進(jìn)一步建立了所得估計(jì)的大樣本性質(zhì)。大量的數(shù)值模擬分析和實(shí)例應(yīng)用都驗(yàn)證了所提估計(jì)方法的有效性。(2)為了克服縱向數(shù)據(jù)中多元協(xié)變量的維數(shù)禍根問題,我們?cè)诘谌卵芯苛司哂薪稻S功效的縱向數(shù)據(jù)單指標(biāo)模型的估計(jì)問題�；趩汤锼够纸夂途植烤�性估計(jì)方法構(gòu)造了一個(gè)新的有效的估計(jì)過程來得到縱向數(shù)據(jù)單指標(biāo)模型中的非參和參數(shù)部分的估計(jì),并建立了它們的漸近正態(tài)性。數(shù)值模擬和實(shí)例分析都證實(shí)了所提估計(jì)方法的穩(wěn)定性和優(yōu)良性。(3)血管通路對(duì)于腎透析的病人至關(guān)重要,已有的醫(yī)學(xué)研究表明血管通路CVC常會(huì)引發(fā)感染且對(duì)透析后的血液含量有不好的影響,而轉(zhuǎn)換為血管通路AVF對(duì)病人有很好的治療效果。我們感興趣的轉(zhuǎn)換血管通路的動(dòng)態(tài)影響以及是否與轉(zhuǎn)換時(shí)間有關(guān)等問題還沒有相應(yīng)的統(tǒng)計(jì)研究,進(jìn)一步此類縱向數(shù)據(jù)分析需要包含多個(gè)時(shí)間指標(biāo)變量。針對(duì)這一系列的問題,在第四章我們構(gòu)造了一個(gè)一般化的靈活的模型,它能同時(shí)刻畫處理方式轉(zhuǎn)換的動(dòng)態(tài)影響、相關(guān)協(xié)變量的動(dòng)態(tài)影響以及隨著處理方式時(shí)間、日歷時(shí)間和轉(zhuǎn)換時(shí)間的變化趨勢(shì),且關(guān)心的轉(zhuǎn)換影響依賴于轉(zhuǎn)換時(shí)間和轉(zhuǎn)換后的時(shí)間�；诰植烤�性估計(jì)和回切的估計(jì)過程,得到了模型中所有未知函數(shù)的估計(jì)。同時(shí)也研究了所得到的估計(jì)的大樣本性質(zhì)。數(shù)值模擬驗(yàn)證了所提方法的良好的有限樣本表現(xiàn)。最后將所提的模型和估計(jì)方法應(yīng)用到了探究透析病人轉(zhuǎn)換血管通路對(duì)其血液中白蛋白(albumin)的動(dòng)態(tài)影響。統(tǒng)計(jì)分析結(jié)果顯示透析病人血管通路從CVC轉(zhuǎn)換為AVF能夠提高其血液中白蛋白(albumin)的含量且越早轉(zhuǎn)換越好。(4)由血管通路引發(fā)的并發(fā)癥是導(dǎo)致腎透析病人高的住院率和死亡率的主要原因之一,從而也導(dǎo)致了高額的醫(yī)療費(fèi)用。因此,在第四章的基礎(chǔ)上,我們?cè)诘谖逭卵芯客肝霾∪宿D(zhuǎn)換血管通路對(duì)其住院情況的動(dòng)態(tài)影響。針對(duì)這一問題,我們構(gòu)造了一個(gè)一般化的靈活的處理方式轉(zhuǎn)換影響的廣義模型。基于局部擬似然和局部線性估計(jì)方法,得到了模型中所有未知函數(shù)的非參估計(jì),同時(shí)給出了它們的大樣本性質(zhì)。數(shù)值模擬和實(shí)例數(shù)據(jù)分析進(jìn)一步驗(yàn)證了所提方法的有效性。詳盡的統(tǒng)計(jì)分析結(jié)果顯示透析病人血管通路從CVC轉(zhuǎn)換為AVF能有效地降低其住院率,且與轉(zhuǎn)換時(shí)間有關(guān)。我們的方法同樣適用于其它的處理方式改變的問題研究。本文的結(jié)論和方法豐富了縱向數(shù)據(jù)下非參半?yún)⒒貧w模型的估計(jì)方法,將有助于分析在經(jīng)濟(jì)學(xué)、生物統(tǒng)計(jì)等應(yīng)用領(lǐng)域中遇到的復(fù)雜多變的問題。
[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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O212.7
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