In this paper, we develop a statistical group sparse beamforming framework to minimize the network power consumption for green cloud radio access networks (Cloud-RANs). It will promote group sparsity structures in the beamforming vectors, which will provide a good indicator for remote radio head (RRH) ordering to enable adaptive RRH selection for power saving. In contrast to the previous works that depend heavily on instantaneous channel state information (CSI), the proposed algorithm only depends on the long-term channel state attenuation for RRH ordering, which does not require frequent update, thereby significantly reducing the computation overhead. This is achieved by developing a smoothed ℓp-minimization approach to induce group sparsity in beamforming vectors, followed by an iterative reweighted-ℓ2 algorithm via the principles of the majorization-minimization (MM) algorithm and the Lagrangian duality theory. With the well-structured closed-form solutions at each iteration, we further leverage the large-dimensional random matrix theory to derive deterministic approximations for the squared ℓ2-norm of the induced group sparse beamforming vectors in the large system regimes. The deterministic approximation results only depend on statistical CSI and will guide the RRH ordering. Simulation results demonstrate the near-optimal performance of the proposed algorithm, even in finite systems.