广义线性模型中基于自适应弹性网的变量选择
发布时间：2019-06-05 05:01
【摘要】：广义线性模型是统计学中非常重要的模型之一,它在生物、经济、医学、社会等领域有着广泛地应用。在实际建模过程中,一开始往往选择的自变量较多,如何从中选取真正对因变量有关系的变量,是变量选择研究中关心的问题.因此讨论广义线性模型下的变量选择,具有较强的应用价值和实践意义.本文主要借助自适应弹性网估计方法讨论广义线性模型的变量选择问题。首先给出广义线性模型下参数的自适应弹性网估计方法;然后借助此估计方法,给出广义线性模型的变量选择算法;接着从理论上给出广义线性模型下自适应弹性网估计方法的统计性质,如渐近正态性、弱相合性、稀疏性及组间效应等,通过这些性质说明自适应弹性网估计满足Oracle性质,且能够解决变量间具有很强相关性的变量问题;最后通过模拟与常用的变量选择方法,如岭回归、Lasso、自适应Lasso和弹性网估计方法进行比较,模拟结果显示,在BIC准则下,自适应弹性网估计方法比其它常用的变量选择方法有一定的优势,即其选择出来的模型更接近于真实的模型。
[Abstract]:Generalized linear model is one of the most important models in statistics, which is widely used in biology, economy, medicine, society and other fields. In the process of actual modeling, there are often many independent variables selected at the beginning. How to select the variables that are really related to dependent variables is a concern in the study of variable selection. Therefore, it is of great application value and practical significance to discuss the variable selection under the generalized linear model. In this paper, the variable selection problem of generalized linear model is discussed by means of adaptive elastic net estimation method. Firstly, the adaptive elastic net estimation method of parameters under the generalized linear model is given, and then the variable selection algorithm of the generalized linear model is given with the help of this estimation method. Then the statistical properties of adaptive elastic net estimation method under generalized linear model are given theoretically, such as asymptotically normality, weak consistency, sparsity and inter-group effect. These properties show that adaptive elastic net estimation satisfies Oracle property. And it can solve the variable problem with strong correlation between variables. Finally, the simulation is compared with the commonly used variable selection methods, such as ridge regression, Lasso, adaptive Lasso and elastic net estimation. The simulation results show that under the BIC criterion, The adaptive elastic network estimation method has some advantages over other commonly used variable selection methods, that is, the selected model is closer to the real model.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212;F224
本文编号：2493273
[Abstract]:Generalized linear model is one of the most important models in statistics, which is widely used in biology, economy, medicine, society and other fields. In the process of actual modeling, there are often many independent variables selected at the beginning. How to select the variables that are really related to dependent variables is a concern in the study of variable selection. Therefore, it is of great application value and practical significance to discuss the variable selection under the generalized linear model. In this paper, the variable selection problem of generalized linear model is discussed by means of adaptive elastic net estimation method. Firstly, the adaptive elastic net estimation method of parameters under the generalized linear model is given, and then the variable selection algorithm of the generalized linear model is given with the help of this estimation method. Then the statistical properties of adaptive elastic net estimation method under generalized linear model are given theoretically, such as asymptotically normality, weak consistency, sparsity and inter-group effect. These properties show that adaptive elastic net estimation satisfies Oracle property. And it can solve the variable problem with strong correlation between variables. Finally, the simulation is compared with the commonly used variable selection methods, such as ridge regression, Lasso, adaptive Lasso and elastic net estimation. The simulation results show that under the BIC criterion, The adaptive elastic network estimation method has some advantages over other commonly used variable selection methods, that is, the selected model is closer to the real model.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212;F224
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