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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/65497


    Title: A class of generalized ridge estimator for high-dimensional linear regression
    Authors: 楊思芃;Yang,Szu-peng
    Contributors: 統計研究所
    Keywords: 脊迴歸;高維度資料;Ridge regression;High dimensional;Generalized ridge regression
    Date: 2014-07-24
    Issue Date: 2014-10-15 15:33:16 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 此篇論文建立在多元線性迴歸(Multiple linear regression)模型之上。在這個模型之下,一般常用的最小平方估計量(Least square estimator)並不適合用在變數個數大的情況,會產生共線性(Collinearity)的問題,特別是在變數個數大於樣本數的時候。Hoerl和Kennard在1970年提出了Generalized ridge迴歸方法。在理論上,Generalized ridge估計量可以解決最小平方估計量的共線性問題。其後,也有許多人討論過特殊型式的Generalized ridge估計量。但是,當變數個數增大的時候,需要估計的參數也隨之增加,導致其實行上的困難,因此大多只考慮樣本數大於變數個數的情形。我們在此篇論文提出了一個在高變數個數之下也能運作的Generalized ridge估計量的特殊型。除此之外,此估計量在貝氏理論中也具有適當的解釋,更可以與先驗資訊做連結,藉此取得較佳的估計。在此篇論文中,我們做了顯著性檢定、模擬資料以及實際資料分析。資料分析中,一般的ridge估計量被拿來與我們提出的估計量做比較,而我們提出的估計量以均方差(Mean square error)來說表現得比ridge估計量來得好。;In multiple linear regression, the least square estimator is inappropriate for high-dimensional regressors, especially for p≥n. Consider the linear regression model. The generalized ridge estimator has been considered by many authors under the usual p<=&quot;&quot; with=&quot;&quot; data=&quot;&quot; cancer=&quot;&quot; lung=&quot;&quot; cell=&quot;&quot; non-small=&quot;&quot; the=&quot;&quot; using=&quot;&quot; method=&quot;&quot; demonstrate=&quot;&quot; we=&quot;&quot; p≥n.=&quot;&quot; and=&quot;&quot; p
    Appears in Collections:[統計研究所] 博碩士論文

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