In this work, we propose low-complexity adaptive biased estimation algorithms, called group-based shrinkage estimators (GSEs), for parameter estimation and interference suppression scenarios with mechanisms to automatically adjust the shrinkage factors. The proposed estimation algorithms divide the target parameter vector into a number of groups and adaptively calculate one shrinkage factor for each group. GSE schemes improve the performance of the conventional least squares (LS) estimator in terms of the mean-squared error (MSE), while requiring a very modest increase in complexity. An MSE analysis is presented which indicates the lower bounds of the GSE schemes with different group sizes. We prove that our proposed schemes outperform the biased estimation with only one shrinkage factor and the best performance of GSE can be obtained with the maximum number of groups. Then, we consider an application of the proposed algorithms to single-carrier frequency-domain equalization (SC-FDE) of direct-sequence ultra-wideband (DS-UWB) systems, in which the structured channel estimation (SCE) algorithm and the frequency domain receiver employ the GSE. The simulation results show that the proposed algorithms significantly outperform the conventional unbiased estimator in the analyzed scenarios.