頁籤選單縮合
題 名 | On Block Thresholding in Wavelet Regression: Adaptivity, Block Size, and Threshold Level |
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作 者 | Cai,T. Tony; | 書刊名 | Statistica Sinica |
卷 期 | 12:4 2002.10[民91.10] |
頁 次 | 頁1241-1273 |
分類號 | 319.3 |
關鍵詞 | Block thresholding; Convergence rate; Global adaptivity; Local adaptivity; Minimax estimation; Nonparametric regression; Smoothing parameter; Wavelets; |
語 文 | 英文(English) |
英文摘要 | In this article we investigate the asymptotic and numerical properties of a class of block thresholding estimators for wavelet regression. We consider the effect of block size on global and local adaptivity and the choice of thresholding constant. The optimal rate of convergence for block thresholding with a given block size is derived for both the global and local estimation. It is shown that there are conflicting requirements on the block size for achieving the global and local adaptivity. We then consider the choice of thresholding constant for a given block size by treating the block thresholding as a hypothesis testing problem. The combined results lead naturally to an optimal choice of block size and thresholding constant. We conclude with a numerical study which compares the finite-sample performance among block thresholding estimators as well as with other wavelet methods. |
本系統中英文摘要資訊取自各篇刊載內容。