We propose a parameter shrinkage adaptation framework to estimate models with only a limited set of adaptation data to improve accuracy for automatic speech recognition, by regularizing an objective function with a sum of parameter-wise power q constraint. For the first attempt, we formulate ridge maximum likelihood linear regression (MLLR) and ridge constraint MLLR (CMLLR) with an element-wise square sum constraint to regularize the objective functions of the conventional MLLR and CMLLR, respectively. Tested on the 5k-WSJ0 task, the proposed ridge MLLR and ridge CMLLR algorithms give significant word error rate reduction from the errors obtained with standard MLLR and CMLLR in an utterance-by-utterance unsupervised adaptation scenario.