頁籤選單縮合
題 名 | On Design-Weighted Local Fitting and Its Relation to the Horvitz-Thompson Estimator |
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作 者 | Einbeck, Jochen; Augustin Thomas; | 書刊名 | Statistica Sinica |
卷 期 | 19:1 2009.01[民98.01] |
頁 次 | 頁103-123 |
分類號 | 319 |
關鍵詞 | Bias reduction; Horvitz-Thompson estimator; Kernel smoothing; Leverage values; Local polynomial modelling; Nonparametric smoothing; Stratification; |
語 文 | 英文(English) |
英文摘要 | Abstract: Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze design-weighted versions of the well-known local polynomial regression estimators, derive their asymptotic bias and variance, and observe that the asymptotically optimal weights are in conflict with (practically motivated) weighting schemes previously proposed in the literature. We investigate this conflict using theory and simulation, and find that the problem has a surprising counterpart in sampling theory, leading us back to the discussion on the Horvitz-Thompson estimator and Basu's (1971) elephants. In this light one might consider our results as an asymptotic and nonparametric version of the Horvitz-Thompson theorem. The crucial point is that bias-minimizing weights can make estimators extremely vulnerable to outliers in the design space and have therefore to be used with particular care. |
本系統中英文摘要資訊取自各篇刊載內容。