Logistic可加部分线性模型的渐近正态性
发布时间：2019-04-26 14:26
【摘要】：广义可加部分线性模型由广义线性模型衍生而来,在其基础上,增加了可加非线性部分,这使得广义可加部分线性模型具备了非参数模型和参数模型的优点.广义可加部分线性模型既具备处理离散型数据的能力,如处理计数数据和属性数据等,又可以通过对非参数部分的处理,增强数据信息的利用,进而在实际的运用时,使预测更加准确.在处理纵向数据时,广义可加部分线性模型同样也具有相应的广义估计方程.纵向数据经常出现在经济学、社会学和医药研究等方面.伴随着大数据的时代的到来,纵向数据的结构也变得复杂,维度也相应的增加,甚至是高维的,这就产生了所谓的“维数祸根”.在普通的回归模型下,一般情况研究是在样本容量趋于无穷,协变量维度固定的条件下进行的.因此研究维数发散的纵向数据具有一定学术价值.本文对样本容量n→∞,协变量维度m发散的Logistic可加部分线性纵向数据模型,通过拓扑同胚定理、样条函数、李雅普诺夫中心极限定理和中值定理等方法,在较弱的条件下证明了其广义估计方程估计的渐近存在性,相合性和渐近正态性.改进了文献中的相应结果.
[Abstract]:The generalized additive partial linear model is derived from the generalized linear model. On the basis of the generalized additive partial linear model, the additive nonlinear part is added, which makes the generalized additive partial linear model have the advantages of non-parametric model and parametric model. The generalized additive partial linear model not only has the ability to deal with discrete data, such as counting data and attribute data, but also can enhance the utilization of data information by processing non-parametric parts. Make the prediction more accurate. When dealing with longitudinal data, the generalized additive partial linear model also has the corresponding generalized estimation equation. Vertical data often appear in economics, sociology and medical research. With the arrival of big data's era, the structure of longitudinal data also becomes complex, the dimension also increases correspondingly, even the high dimension, which produces the so-called "dimension evil root". Under the general regression model, the general case study is carried out under the condition that the sample size tends to infinity and the dimension of covariates is fixed. Therefore, it has some academic value to study the longitudinal data of dimension divergence. In this paper, we use topological homeomorphism theorem, spline function, Lyapunov central limit theorem and median theorem for the Logistic additive partial linear longitudinal data model with sample size n ~ 鈭，
本文编号：2466147
[Abstract]:The generalized additive partial linear model is derived from the generalized linear model. On the basis of the generalized additive partial linear model, the additive nonlinear part is added, which makes the generalized additive partial linear model have the advantages of non-parametric model and parametric model. The generalized additive partial linear model not only has the ability to deal with discrete data, such as counting data and attribute data, but also can enhance the utilization of data information by processing non-parametric parts. Make the prediction more accurate. When dealing with longitudinal data, the generalized additive partial linear model also has the corresponding generalized estimation equation. Vertical data often appear in economics, sociology and medical research. With the arrival of big data's era, the structure of longitudinal data also becomes complex, the dimension also increases correspondingly, even the high dimension, which produces the so-called "dimension evil root". Under the general regression model, the general case study is carried out under the condition that the sample size tends to infinity and the dimension of covariates is fixed. Therefore, it has some academic value to study the longitudinal data of dimension divergence. In this paper, we use topological homeomorphism theorem, spline function, Lyapunov central limit theorem and median theorem for the Logistic additive partial linear longitudinal data model with sample size n ~ 鈭，
本文编号：2466147
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