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In this paper, by using the properties of the higher order statistics (HOS) of speech and noise signals, we develop an improved voice activity detection (VAD) scheme. The proposed scheme employs the logarithm of the kurtosis of the LPC residual of a speech signal and is shown to be more effective and efficient in detecting active speech in medium to low signal-to-noise ratio (SNR) conditions without being unduly affected by the variations in the signal energy. To overcome the inability of the HOS in detecting unvoiced speech, another metric (the low band to full band energy ratio) is introduced. Depending on the estimated mean SNR, the proposed scheme works adaptively in two modes: a simple mode using only the SNR, and an enhanced mode using the HOS, the low band to full band energy ratio and the SNR. This scheme is capable of avoiding unnecessary computations, while maintaining the same performance as that working only in the enhanced mode. Simulations results are presented to demonstrate the effectiveness of the proposed voice activity detection scheme.