【摘要】：廣義線性模型是統(tǒng)計(jì)學(xué)中非常重要的模型之一,它在生物、經(jīng)濟(jì)、醫(yī)學(xué)、社會(huì)等領(lǐng)域有著廣泛地應(yīng)用。在實(shí)際建模過程中,一開始往往選擇的自變量較多,如何從中選取真正對(duì)因變量有關(guān)系的變量,是變量選擇研究中關(guān)心的問題.因此討論廣義線性模型下的變量選擇,具有較強(qiáng)的應(yīng)用價(jià)值和實(shí)踐意義.本文主要借助自適應(yīng)彈性網(wǎng)估計(jì)方法討論廣義線性模型的變量選擇問題。首先給出廣義線性模型下參數(shù)的自適應(yīng)彈性網(wǎng)估計(jì)方法;然后借助此估計(jì)方法,給出廣義線性模型的變量選擇算法;接著從理論上給出廣義線性模型下自適應(yīng)彈性網(wǎng)估計(jì)方法的統(tǒng)計(jì)性質(zhì),如漸近正態(tài)性、弱相合性、稀疏性及組間效應(yīng)等,通過這些性質(zhì)說明自適應(yīng)彈性網(wǎng)估計(jì)滿足Oracle性質(zhì),且能夠解決變量間具有很強(qiáng)相關(guān)性的變量問題;最后通過模擬與常用的變量選擇方法,如嶺回歸、Lasso、自適應(yīng)Lasso和彈性網(wǎng)估計(jì)方法進(jìn)行比較,模擬結(jié)果顯示,在BIC準(zhǔn)則下,自適應(yīng)彈性網(wǎng)估計(jì)方法比其它常用的變量選擇方法有一定的優(yōu)勢(shì),即其選擇出來的模型更接近于真實(shí)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.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212;F224

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