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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/32855


    Title: 單調迴歸的最小平方估計
    Other Titles: Least square estimation for monotone regression
    Authors: 鄭欣怡;Cheng, Hsin-yi
    Contributors: 淡江大學數學學系碩士班
    溫啟仲;Wen, Chi-chung
    Keywords: 單調迴歸;伯氏多項式;懲罰函數法;Monotone Regression;Bernstein Polynomial;Penalty Function Method
    Date: 2009
    Issue Date: 2010-01-11 02:51:58 (UTC+8)
    Abstract: 對於單調迴歸函數,尋求一個簡單、平滑及有效的估計是受到相當大關注。在本論文中,我們使用伯氏多項式來模型化迴歸函數,並以最小平方法來來估計單調迴歸函數。我們使用交叉驗證法來決定伯氏多項式的階數,提出一個以懲罰函數法為原理之演算法來計算所提估計,並提供迴歸函數之單點信賴帶的估計。模擬試驗及實際資料分析說明了此統計方法的可行性。
    Search for a simple, smooth and efficient estimate of a smooth monotone regression function is of considerable interest. In this thesis, we describe a least square method for monotone regression in which the regression function is modeled by the Bernstein polynomial. We employ the cross-validation criterion to determine the degree of Bernstein polynomial, propose a penalty function method based algorithm to compute estimate and provide a pointwise confidence band for regression function. The success of this method is demonstrated in simulation studies and in an analysis of real data.
    Appears in Collections:[數學學系暨研究所] 學位論文

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