A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series

Roueff and Taqqu ( 2009a ) prove that this asymptotic normality is acquired in univariate setting, but no result was provided for wavelet- based estimation in multivariate setting..

Keywords: Estimator selection, Model selection, Variable selection, Linear estimator, Kernel estimator, Ridge regression, Lasso, Elastic net, Random Forest, PLS1

Lastly, we propose a model selection strategy relying on a Goldenschluger and Lepski [21] method and prove a risk bound for the nal estimator: this result holds for

Thanks to a given noise level δ and a well-suitable inte- gration length window, we show that the derivative estimator error can be O (δ n+1+q q+1 ) where q is the order of

Keywords and phrases: Pointwise mean squared error, Wavelet methods, Density estimation, Nonparametric

It is important to mention that the rate of convergence (ln n/n) 2s/(2s+2δ+1) is the near optimal one in the minimax sense for f b (not b g) under the MISE over Besov balls for

Considering the weak dependent case on the observations, we prove a general result on the rate of convergence attains by a hard wavelet thresholding estimator under the MISE over

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