Earticle

A hybrid denoising method is presented as a combination of Empirical Mode Decomposition (EMD) and Higher Order Statistics (HOS). EMD, an adaptive data-driven method, is used for effective decomposition of a noisy signal into its functional components. Then Kurtosis and Bispectrum operate as Gaussianity estimators, supplemented by Bootstrap techniques, ensuring detection and removal of the signal’s Gaussian components. Thresholding techniques are used at the final step for maximum suppression of signal noise, where thresholds are set by estimating the long-term correlation of the corrupting colored noise in the form of the Hurst exponent. Experimental results prove the applicability of the method in signal denoising. Specifically, EMD-HOS outperforms similar denoising techniques based on Wavelets for the most types of test signals.

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.