On the Minimax Optimality of Block Thresholded Wavelet Estimators with Long Memory Data
نویسندگان
چکیده
We consider the estimation of nonparametric regression function with long memory data and investigate the asymptotic rates of convergence of estimators based on block thresholding. We show that the estimators achieve optimal minimax convergence rates over a large class of functions that involve many irregularities of a wide variety of types, including chip and Doppler functions, and jump discontinuities. Therefore, in the presence of long memory noise, wavelet estimators still provide extensive adaptivity to many irregularities of large function classes. Short title: Wavelet estimator with long memory data 2000 Mathematics Subject Classification: Primary: 62G07; Secondary: 62C20
منابع مشابه
On the Minimax Optimality of Block Thresholded Wavelets Estimators for ?-Mixing Process
We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...
متن کاملAdapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric density model, we show that the resulting estimator is optimal in the minimax sense over all Besov balls under the L2 risk, without any logarithm factor.
متن کاملAdapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators . Christophe Chesneau and Guillaume Lecué
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric density model, we show that the resulting estimator is optimal in the minimax sense over all Besov balls under the L2 risk, without any logarithm factor.
متن کاملOn Block Thresholding in Wavelet Regression with Long Memory Correlated Noise
Johnstone and Silverman (1997) and Johnstone (1999) described a level-dependent thresholding method for extracting signals from both shortand long range dependent noise in the wavelet domain structure. It is shown that their Stein unbiased risk estimators (SURE) attain the exact optimal convergence rates in a wide range of Besov balls in certain asymptotic models of standard sample-data models....
متن کاملMinimax Wavelet Estimation Via Block Thresholding
Wavelet shrinkage methods have been very successful in nonparametric regression. The most commonly used wavelet procedures achieve adaptivity through term-by-term thresholding. The resulting estimators attain the minimax rates of convergence up to a logarithmic factor. In the present paper, we propose a block thresholding method where wavelet coef-cients are thresholded in blocks, rather than i...
متن کامل