In this study, a family of coefficient adaptation methods for speech recognition under white noise environments is proposed. Based on the property of speech cepstral vector shrinking under white noise influence, the noisy speech reference cepstral vector can be approximated by a linear shrunk version of its clean counterpart. This approximation induces an affine transformation on delta cepstral vector to approximate its noisy version. Using these approximations, an adaptive HMM is proposed for noisy speech recognition. Three alternate adaptation schemes will be also investigated. The adaptation parameters can be determined by searching for optimal values such that the adapted reference is the closest to the test one. In addition, a bilinear function of log-signal-ratio is also proposed to determine the linear shrinking factor. The experimental results show that the proposed adaptation methods can compensate the noise effect.