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題名 | 估計母體特定區域的核估計方法= |
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作者 | 柯文定; |
期刊 | 中國統計學報 |
出版日期 | 19951200 |
卷期 | 33:4 1995.12[民84.12] |
頁次 | 頁549-562 |
分類號 | 319.51 |
語文 | chi |
關鍵詞 | 特定區域; 無母數迴歸分析; 樣本均方差; 核估計量; 交互驗證法; Region of interest; Nonparametric regression; Sample mean squared error; Kernel estimator; Cross-validation; |
中文摘要 | 在等距離分布固定取樣的無母數迴歸分析模型中,本主介紹一個二階段式的核估計方法來估計母體特定區域,例如母體迴歸函數值大於某特定值的區域。這個核估計方法的第一階段是用核估計量 (kernel estimator) 來找此特定區域,其中所 使用的帶寬值 (bandwidth) 是用交互驗證法 (cross- validation) 所產生的帶寬估計值。第二階段仍是用此核估計量來找該特定區域,只是此時所用的帶寬值是將交互驗證法應用到第一階段所得到的特定區域估計值上面的資料所產生的帶寬估計值。模擬研究顯示第二階段所得到的特定區域估計值會比第一階段所得到的特定區成估計值有較小的樣本均方差 (sample mean squared error),同時前者也比一個簡單 (naive) 方法所產生的特定區域估計值有更小的樣本均方差。此簡單方法即是直接用反應變數值 (responses) 來找此特定區域。 |
英文摘要 | For the equally spaced fixed design nonparametric regression, a two-stage kernel type estimator for the region where the underlying regression function has properties of interest is proposed. For example, the region is taken as the set of design points where the values of the regression function are larger than a given value. The first stage of the estimation is to take the region where the kernel regression function estimator has the properties of interest. Here the bandwidth used is the cross-validated bandwidth. The second stage of the kernel type estimator does the same job, but the bandwidth used is produced by applying cross-validation to the region generated by the first stage kernel type estimator. Simulation studies show that the region estimated by the second stage kernel type estimator performs better than that. produced by the first stage kernel type estimator, in the sense of the sample mean square error. The proposed estimator also performs better than a naive method. The naive method is to estimate the region by the set. of design points where the responses satisfy the conditions of interest.. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。