This work presents a robust algorithm for voice activity detection (VAD) and noise reduction mechanism using combined properties of higher-order statistics (HOS) and an efficient algorithm to estimate the instantaneous Signal-to-Noise Ratio (SNR) of speech signal in a background of acoustic noise. The flat spectral feature of Linear Prediction Coding (LPC) residual results in distinct characteristics for the cumulants in terms of phase, periodicity and harmonic content and yields closed-form expressions for the skewness and kurtosis. The HOS of speech is immune to Gaussian noise and this makes them particularly useful in algorithms designed for low SNR environments. The proposed algorithm uses HOS and smooth power estimate metrics with second-order measures, such as SNR and LPC prediction error, to identify speech and noise frames. A voicing condition for speech frames is derived based on the relation between the skewness, kurtosis of voiced speech and estimate of smooth noise power. The algorithm presented and its performance is compared to HOS-only based VAD algorithm. The results show that the proposed algorithm has an overall better performance, with noticeable improvement in Gaussian-like noises, such as street and garage, and high to low SNR, especially for probability of correctly detecting speech. The proposed algorithm is replicated on DSK C6713.