This paper proposes a noise-biased compensation of minimum statistics (MS) method using a nonlinear function and a priori speech absence probability (SAP) for speech enhancement in highly nonstationary noisy environments. The MS method is a well-known technique for noise power estimation in nonstationary noisy environments; however, it tends to bias noise estimation below that of the true noise level. The proposed method is combined with an adaptive parameter based on a sigmoid function and a priori SAP for residual noise reduction. Additionally, our method uses an autoparameter to control the trade-off between speech distortion and residual noise. We evaluate the estimation of noise power in highly nonstationary and varying noise environments. The improvement can be confirmed in terms of signal-to-noise ratio (SNR) and the Itakura-Saito Distortion Measure (ISDM).