頁籤選單縮合
題 名 | Multivariate Wavelet Thresholding in Anisotropic Function Spaces |
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作 者 | Neumann,Michael H.; | 書刊名 | Statistica Sinica |
卷 期 | 10:2 2000.04[民89.04] |
頁 次 | 頁399-431 |
分類號 | 319.5 |
關鍵詞 | Anisotropic smoothness classes; Anisotropic wavelet basis; Multivariate wavelet estimators; Nonlinear thresholding; Nonparametric curve estimation; Optimal rate of convergence; Smoothness classes with dominating mixed derivatives; |
語 文 | 英文(English) |
英文摘要 | It is well known that multivariate curve estimation under standard (isotropic) smoothness conditions suffers from the “curse of dimensionality” this is reflected by rates of convergence that deteriorate seriously in standard asymptotic settings. Better rates of convergence than those corresponding to isotropic smoothness priors are possible if the curve to be estimated has different smoothness properties in different directions and the estimation scheme is capable of making use of a lower complexity in some of the directions. We consider typical cases of anisotropic smoothness classes and explore how appropriate wavelet estimators can exploit such restrictions on the curve that require and adaptation to different smoothness properties in different. It turns out that nonlinear thresholding with an anisotropic multivariate wavelet basis leads to optimal rated of convergence under smoothness priors of anisotropic type. We derive asymptotic results in the model “signal plus Gaussian white noise”, where a decreasing noise level mimics the standard asymptotics with increasing sample size. |
本系統中英文摘要資訊取自各篇刊載內容。