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題名 | On Derivative Estimation in Spline Regression |
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作者 | Zhou,Shanggang; Wolfe,Douglas A.; | 書刊名 | Statistica Sinica |
卷期 | 10:1 2000.01[民89.01] |
頁次 | 頁93-108 |
分類號 | 319.51 |
關鍵詞 | 樣條迴歸; 漸近正態性; Asymptotic bias; Asymptotic normality; Asymptotic variance; Bernoulli polynomial; B-splines; Derivative estimators; Heteroscedastic errors; Random designs; Regression splines; |
語文 | 英文(English) |
英文摘要 | We consider the problem of estimating the derivatives of a regression function by the corresponding derivatives of regression splines. Unlike kernel smoothers, these spline derivative estimators do not have boundary problems. In addition, they have simple expressions and are easy to compute. In this paper, we study the local asymptotic properties of these derivative estimators. Under regularity conditions, the asymptotic bias and variance of these estimators are derived, and asymptotic normality is established. Furthermore, we extend the results to random designs and heteroscedastic errors. |
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