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In this letter, we develop a robust voice activity detector (VAD) for the application to variable-rate speech coding. The developed VAD employs the decision-directed parameter estimation method for the likelihood ratio test. In addition, we propose an effective hang-over scheme which considers the previous observations by a first-order Markov process modeling of speech occurrences. According to our simulation results, the proposed VAD shows significantly better performances than the G.729B VAD in low signal-to-noise ratio (SNR) and vehicular noise environments.