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This paper presents a method based on higher order statistics (HOS), namely the normalized third-order moment (skewness), for blind estimation of the inverse filter of the room impulse response (RIR). Skewness is used as a measure of asymmetry, and a comprehensive comparison with the commonly used metric (kurtosis) is presented. It is shown that a sufficiently long linear predictive (LP) residual of the speech signal has an asymmetric pdf with sufficient skewness to be used as a score function for the HOS-based approach. The proposed algorithm is optimized for the inverse filter estimation problem. This optimization includes an efficient initialization for high reverberation intensities, enabling the method to be employed in highly reverberant rooms. The direct-to-reverberation ratio (DRR) as well as the equalized impulse response clearly show that our method can estimate the inverse filter even in highly reverberant environments. In addition, performance results using recorded background noise and in time-varying environments illustrate that our approach is applicable in real world situations. The proposed method is shown to be superior to the method by Wu and Wang, particularly in terms of reducing the coloration effect. Experiments under different acoustic conditions confirm the effectiveness of the proposed method for time delay estimation (TDE). Finally, the proposed algorithm is used as the first-stage of monaural segregation, and it is shown to improve the performance under different conditions.