几类变系数模型的统计推断及其应用研究

发布时间：2018-06-19 14:41

本文选题：自适应保跳回归 + 核光滑方法　；参考：《东南大学》2016年博士论文

【摘要】：本文主要研究了几类变系数模型的统计推断及应用问题,包括带有跳不连续系数的变系数模型的估计、时变系数模型的跳检测和系数估计、具有异方差的半变系数模型的正交估计、半变系数模型的异方差检验和纵向数据下半变系数模型的估计.主要内容如下：第一章着重介绍几类变系数模型的研究背景、研究意义、研究现状和存在的问题.另外,大致陈述了本文的主要工作,并阐释了本文的主要创新点.第二章研究带有跳不连续系数的变系数模型的估计.基于局部线性光滑和保跳回归技术,我们提出了自适应保跳估计方法来估计系数函数.所提出的方法不需要知道跳点的位置和个数,也不需要进行任何的假设检验,便可自动地识别系数中的跳点并估计系数函数.在一些比较弱的假设条件下,建立了自适应保跳估计量的渐近性质,并通过数值模拟评价了它的有限样本性质.最后通过一个实例分析验证了所提出方法的有效性.第三章研究时变系数模型的跳检测和系数估计.在实际应用中,潜在的系数曲线可能有奇异点,包括某些未知的位置上有跳点和某些相关过程的结构变点.检测这些奇异点对于了解结构改变是非常重要的.基于局部多项式技术和函数二阶导数的零穿越性质,我们提出一个跳检测方法来检测系数函数中的跳点.然后,利用检测到的跳点提出了曲线估计方法.进一步地,我们讨论了程序参数的选择,并在一些弱的条件下建立了估计量在连续区间和跳点邻域内的渐近性质.最后,通过蒙特卡洛试评价所提出方法的有限样本表现,并通过两个实例分析说明了该方法的用途.第四章讨论了具有异方差的半变系数模型的正交估计.基于矩阵的正交投影、局部线性估计和加权最小二乘估计,我们提出了一个容易实施的迭代两阶段正交投影估计方法,来估计模型的参数系数、非参数系数和方差函数.所得到的参数估计量和非参数估计量相互不受影响.在比较弱的假设条件下,建立了它们的相合性和渐近正态性.然后,实施仿真模拟评价了这些估计量的有限样本性质,并通过实例分析说明了所提出方法的有效性.第五章讨论了半变系数模型的异方差检测.在回归模型中检验方差异是非常重要的,因为参数的有效推断要求把异方差考虑在内.本章提出两类异方差检验方法：一类是基于正态误差残差构造检验统计量,另一类是利用检验异方差等价于检验常数均值的伪残差的思想构造检验统计量.然后,用不同速率对应同方差的原假设和备择假设建立了检验统计量的渐近正态性.进一步地,通过数值模拟评价了所提出检验统计量的有限样本表现,并通过实例分析说明该检验的有效性.第六章研究了纵向数据下半变系数模型的估计.半参数光滑方法通常被用来建模纵向数据,我们的兴趣是提高参数系数的效率.基于矩阵的QR分解、局部线性技术、拟得分估计和拟最大似然估计,提出了一个两阶段正交估计方法,来估计模型中的参数系数、非参数系数和协方差函数.所提出的方法可以单独实施,并且所得的估计量相互不影响.在一些弱的假设条件下,给出了估计量的渐近性质.尤其讨论了系数函数在边界处的渐近行为.然后,通过数值模拟评价了估计量的有限样本表现,最后将提出的方法应用于分析AIDS数据.
[Abstract]:This paper mainly studies the statistical inference and application problems of several variable coefficient models, including the estimation of the variable coefficient model with the jump discontinuous coefficient, the jump detection and coefficient estimation of the time-varying coefficient model, the orthogonal estimation of the semi variable coefficient model with heteroscedasticity, the heteroscedasticity test of the semi variable coefficient model and the semi variable coefficient model under the longitudinal data. The main contents are as follows: the first chapter focuses on the research background of several variable coefficient models, research significance, research status and existing problems. In addition, the main work of this paper is described roughly, and the main innovation of this paper is explained. The second chapter studies the estimation of the variable coefficient model with the noncontinuous coefficient of jumping. We propose an adaptive hopping estimation method to estimate the coefficient function. The proposed method does not need to know the position and number of jumping points, and does not need any hypothesis test. It can automatically identify the jump points in the coefficient and estimate the coefficient function. Under some weak assumptions, the method is established. The asymptotic property of adaptive hopping estimator is given and its finite sample properties are evaluated by numerical simulation. Finally, an example is made to verify the effectiveness of the proposed method. The third chapter studies the jump detection and coefficient estimation of the time-varying coefficient model. In practical applications, the potential coefficient curves may have singularity, including some of them. In the unknown position, there are jumps and structural changes in some related processes. Detecting these singularities is very important for understanding structural changes. Based on the local polynomial technique and the zero crossing property of the two order derivative of the function, we propose a jump detection method to detect the jump points in the coefficient function. Then, the detected jump points are proposed. Further, we discuss the selection of the parameters of the program and establish the asymptotic properties of the estimator in the continuous interval and the neighborhood of the jump point in some weak conditions. Finally, the finite sample performance of the proposed method is evaluated by the Monte Carlo method, and the use of the method is illustrated by two examples. Fourth In this chapter, the orthogonal estimation of a semi variable coefficient model with heteroscedasticity is discussed. Based on the orthogonal projection of the matrix, the local linear estimation and the weighted least square estimation, we propose an easy to implement iterative two phase orthogonal projection method to estimate the parameter coefficient, the nonparametric coefficient and the variance function. The measurement and nonparametric estimators are not affected each other. Under the weaker hypothesis, their consistency and asymptotic normality are established. Then, the finite sample properties of these estimators are evaluated by the simulation simulation, and the effectiveness of the proposed method is illustrated by an example. The fifth chapter discusses the different square of the semi variable coefficient model. Difference detection is very important in the regression model, because the effective inference of the parameters is required to take the heteroscedasticity into consideration. In this chapter, two kinds of heteroscedasticity test methods are proposed: one is based on the normal error residual structure test statistics and the other is to use the idea of testing the pseudo residuals equivalent to the mean of the test constant. Then, the asymptotic normality of the test statistics is established by using the original hypothesis and the optional hypothesis of the same variance at different rates. Further, the finite sample performance of the test statistics is evaluated by numerical simulation, and the validity of the test is illustrated by an example. The sixth chapter studies the longitudinal data. The estimation of semi variable coefficient model. Semi parametric smoothing method is usually used to model the longitudinal data. Our interest is to improve the efficiency of parameter coefficients. Based on the matrix QR decomposition, local linear technology, quasi score estimation and quasi maximum likelihood estimation, a two stage orthogonality estimator is proposed to estimate the parameter coefficient and non parameter in the model. Coefficients and covariance functions. The proposed method can be implemented separately and the estimated quantities are not affected each other. Under some weak assumptions, the asymptotic behavior of the estimators is given. The asymptotic behavior of the coefficient function at the boundary is discussed especially. Then, the finite sample performance of the estimator is evaluated by numerical simulation. Finally, the performance of the estimator is evaluated. The method is applied to the analysis of AIDS data.
【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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