本文選題：Lasso + Adaptive��； 參考：《廣西大學(xué)》2015年碩士論文

【摘要】：在生存分析中,Cox模型是處理生存數(shù)據(jù)的經(jīng)典模型.隨著大數(shù)據(jù)的盛行,人們面對高維、強相關(guān)生存數(shù)據(jù)的機會越來越多.如何克服傳統(tǒng)Cox模型不能處理上述生存數(shù)據(jù)的缺陷,已成為統(tǒng)計學(xué)界共同關(guān)注的熱點.為解決這一問題,本文將變量選擇中比較重要的兩種方法應(yīng)用于Cox模型中,即Elastic Net方法和Adaptive Elastic Net方法.具體研究內(nèi)容及結(jié)果如下：一方面,由于Elastic Net方法能有效處理高維小樣本、強相關(guān)變量組數(shù)據(jù),本文將其運用于Cox模型的變量選擇中,探討Cox模型下Elastic Net估計的組效應(yīng)性質(zhì),證明得到Elastic Net方法能將強相關(guān)變量組中的變量全部選入模型,即具有組效應(yīng)性質(zhì).通過數(shù)值模擬,驗證了Elastic Net估計具有組效應(yīng)性質(zhì),而Lasso方法無此功效.通過具體實例,肯定了ElasticNet方法運用于Cox模型的可行性,驗證了Elastic Net方法的擬合效果和預(yù)測能力均優(yōu)于逐步法,表明了與Elastic Net方法結(jié)合后的Cox模型優(yōu)于傳統(tǒng)Cox模型.另一方面,由于Adaptive Elastic Net方法對零變量的估計優(yōu)于Elastic Net方法,本文將Adaptive Elastic Net方法運用于Cox模型的變量選擇中,探討Cox模型下Adaptive Elastic Net估計的組效應(yīng)性質(zhì)及Oracle性質(zhì),證明得到Adaptive Elastic Net方法能將強相關(guān)變量全部選入模型,且對零變量的處理更準確,即具有組效應(yīng)性質(zhì)及Oracle性質(zhì).通過數(shù)值模擬,驗證了在擬合效果和精確度方面,Adaptive Elastic Net方法優(yōu)于Lasso方法、Adaptive Lasso方法和Elastic Net方法.
[Abstract]:Cox model is a classical model for dealing with survival data in survival analysis. With the prevalence of big data, there are more and more opportunities for people to face high-dimensional and strongly related survival data. How to overcome the shortcomings of the traditional Cox model which can not deal with the above survival data has become a common concern in the field of statistics. In order to solve this problem, two important methods of variable selection are applied to Cox model, i.e. Elastic net method and Adaptive Elastic net method. The specific contents and results are as follows: on the one hand, Elastic net method can effectively deal with high-dimensional, small-sample and strongly correlated variable set data. In this paper, we apply it to the selection of variables in Cox model, and discuss the group effect properties of Elastic net estimation under Cox model. It is proved that the Elastic net method can select all the variables in the strongly correlated variable group into the model, that is, it has the property of group effect. Numerical simulation shows that Elastic net estimation has group effect property, but Lasso method has no effect. The feasibility of applying Elastic net method to Cox model is confirmed. The fitting effect and prediction ability of Elastic net method are better than that of step by step method. It is shown that the Cox model combined with Elastic net method is superior to the traditional Cox model. On the other hand, because Adaptive Elastic net method is superior to Elastic net method in estimating zero variables, this paper applies Adaptive Elastic net method to variable selection of Cox model, and discusses the group effect property and Oracle property of Adaptive Elastic net estimation under Cox model. It is proved that all strongly correlated variables can be selected into the model by Adaptive Elastic net method, and the processing of zero variables is more accurate, that is, it has group effect property and Oracle property. Numerical simulation shows that adaptive Elastic net method is superior to Lasso method and adaptive Lasso method and Elastic net method in fitting effect and accuracy.
【學(xué)位授予單位】：廣西大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O212.1

【參考文獻】

相關(guān)期刊論文 前1條

1 董英;黃品賢;;Cox模型及預(yù)測列線圖在R軟件中的實現(xiàn)[J];數(shù)理醫(yī)藥學(xué)雜志;2012年06期

，

本文編號：2087369