In this paper, we present a statistical beamforming algorithm as a pre-processing step for robust automatic speech recognition (ASR). By modeling the target speech as a non-stationary Laplacian distribution, a mask-based statistical beamforming algorithm is proposed to exploit both its output and masked input variance for robust estimation of the beamformer. In addition, we also present a method for steering vector estimation (SVE) based on a noise power ratio obtained from the target and noise outputs in independent component analysis (ICA). To update the beamformer in the same ICA framework, we derive ICA with distortionless and null constraints on target speech, which yields beamformed speech at the target output and noises at the other outputs, respectively. The demixing weights for the target output result in a statistical beamformer with the weighted spatial covariance matrix (wSCM) using a weighting function characterized by a source model. To enhance the SVE, the strict null constraints imposed by the Lagrange multiplier methods are relaxed by generalized penalties with weight parameters, while the strict distortionless constraints are maintained. Furthermore, we derive an online algorithm based on an optimization technique of recursive least squares (RLS) for practical applications. Experimental results on various environments using CHiME-4 and LibriCSS datasets demonstrate the effectiveness of the presented algorithm compared to conventional beamforming and blind source extraction (BSE) based on ICA on both batch and online processing.