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.
