Block thresholding for density estimation: local and global adaptivity
نویسندگان
چکیده
منابع مشابه
Density estimation by wavelet thresholding
Density estimation is a commonly used test case for non-parametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coe cients. Minimax rates of convergence are studied over a large range of Besov function classes Bs;p;q and for a range of global L 0 p error measures, 1 p < 1. A single wavelet threshold estimator is asymptotically...
متن کاملWavelet Regression via Block Thresholding : Adaptivity and the Choice of Block Sizeand Threshold
We consider block thresholding rules for wavelet regression and derive an \opti-mal" block thresholding estimator that is fully speciied and easy to implement, at a computational cost of O(n). We begin by studying the eeect of block length on both the global and local adaptiv-ity. The results show that there are connicting requirements on block size for achieving the global and local adaptivity...
متن کاملOn Block Thresholding in Wavelet Regression: Adaptivity, Block Size, and Threshold Level
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 ch oice 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...
متن کاملAdaptive Covariance Matrix Estimation through Block Thresholding
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collectio...
متن کاملBlock thresholding for a density estimation problem with a change-point
We consider a density estimation problem with a change-point. We develop an adaptive wavelet estimator constructed from a block thresholding rule. Adopting the minimax point of view under the Lp risk (with p ≥ 1) over Besov balls, we prove that it is near optimal.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2005
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2004.07.003