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題 名 | Waveshrink with Firm Shrinkage |
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作 者 | Gao,Hong-ye; Bruce,Andrew G.; | 書刊名 | Statistica Sinica |
卷 期 | 7:4 1997.10[民86.10] |
頁 次 | 頁855-874 |
分類號 | 319.51 |
關鍵詞 | Bias estimation; Firm shrinkage; Minimax thresholds; Nonparametric regression; Signal de-noising; Trend estimation; Variance estimation; Wavelet transform; Waveshrink; |
語 文 | 英文(English) |
英文摘要 | Donoho and Johnstone's (1994) WaveShrink procedure has proven valuable for signal de-noising and non-parametric regression. WaveShrink has very broad asymptotic near-optimality properties. In this paper, we introduce a new shrinkage scheme, firm, which generalizes the hard and soft shrinkage proposed by Donoho and Johnstone (1994). We derive derive minimax thresholds and provide formulas for computing the pointwise variance, bias, and risk for WaveShrink with firm shrinkage. We study the properties of the shrinkage functions, and demonstrate that firm shrinkage offers advantages over both hard shrinkage (uniformly smaller risk and less sensitivity to small perturbations in the data) and soft shrinkage (smaller bias and overall L₂ risk). Software is provided to reproduce all results in this paper. |
本系統中英文摘要資訊取自各篇刊載內容。