頁籤選單縮合
題 名 | Uniform Estimation of a Signal Based on Inhomogeneous Data |
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作 者 | Gaïffas, Stéphane; | 書刊名 | Statistica Sinica |
卷 期 | 19:2 2009.04[民98.04] |
頁 次 | 頁427-447 |
分類號 | 319.5 |
關鍵詞 | Adaptive estimation; Minimax theory; Nonparametric regression; Random design; |
語 文 | 英文(English) |
英文摘要 | Abstract: The aim of this paper is to recover a signal based on inhomogeneous noisy data (the amount of data can vary strongly from one point to another.) In particular, we focus on the understanding of the consequences of the inhomogeneity of the data on the accuracy of estimation. For that purpose, we consider the model of regression with a random design, and we consider the minimax framework. Using the uniform metric weighted by a spatially-dependent rate in order to assess the accuracy of estimators, we are able to capture the deformation of the usual minimax rate in situations where local lacks of data occur (the latter are modelled by a design density with vanishing points). In particular, we construct an estimator both design and smoothness adaptive, and we develop a new criterion to prove the optimality of these deformed rates. |
本系統中英文摘要資訊取自各篇刊載內容。