计数数据的广义部分线性可加模型的渐近性质

发布时间：2019-02-13 21:50

【摘要】：随着科学技术的迅猛的发展,现代社会已经进入到大数据时代,我们也被各式各样数量规模庞大的高维数据所包围,尤其是在生物、医药、金融等各个领域中,而这些实际观测结果的干扰因素也是更多的呈现出非线性的作用.因此对高维数据的分析处理也就变得越来越复杂.广义部分线性可加模型(Generalized additive partial linear models,GAPLM)在一般广义线性模型(Generalized linear models,GLM)基础上增加考虑了对结果产生影响的非线性因素,增加了非线性可加项.GAPLM不仅继承了 GLM能同时处理连续、离散等不同数据类型的优良特性,由于增加考虑了非线性干扰因素,因此还能使得对模型的估计预测精度都会有较大的提升,具有一定的应用指导意义.本文所研究的计数数据的广义部分线性可加模型,是响应变量满足Poisson分布的GAPLM,是GLM结合非参数估计的推广.在该模型中同时包含了线性部分和非线性部分,其线性部分的协变量维度可以随着样本容量趋于无穷而趋于无穷,而非参数函数部分则采用多项式样条基的线性组合逼近拟合,可以转化为线性模型来处理,解决了计算上的维数灾难.该文在较弱条件下证明高维纵向计数数据的广义部分线性可加模型估计方程的根的渐近存在性,相合性以及渐近正态性.改进了文献中的相应结果.
[Abstract]:With the rapid development of science and technology, the modern society has entered the era of big data, we are also surrounded by a variety of large quantities of high-dimensional data, especially in biology, medicine, finance and other fields. The interference factors of these observed results are also more nonlinear. Therefore, the analysis and processing of high-dimensional data becomes more and more complex. The generalized partial linear additive model (Generalized additive partial linear models,GAPLM) takes into account the nonlinear factors that affect the results on the basis of the general generalized linear model (Generalized linear models,GLM). The nonlinear additivity is added. GAPLM not only inherits the excellent characteristics that GLM can deal with different data types simultaneously, such as continuous and discrete, but also takes into account the nonlinear disturbance factors. Therefore, the estimation and prediction accuracy of the model can be greatly improved, which has a certain application guidance significance. In this paper, the generalized partially linear additive model of counting data is studied, which is a generalization of GLM combined with nonparametric estimation for the GAPLM, whose response variable satisfies the Poisson distribution. Both linear and nonlinear parts are included in the model. The covariable dimension of the linear part tends to infinity with the sample size approaching infinity, while the nonparametric function part is fitted by linear combination approximation of polynomial spline basis. It can be transformed into a linear model to solve the dimension disaster. In this paper, we prove the asymptotic existence, consistency and asymptotic normality of the root of the estimation equation of the generalized partial linear additive model with high dimensional longitudinal counting data under weaker conditions. The corresponding results in the literature are improved.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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