This paper studies distributed compression for the uplink of a cloud radio access network where multiple multiantenna base stations (BSs) are connected to a central unit, which is also referred to as a cloud decoder, via capacity-constrained backhaul links. Since the signals received at different BSs are correlated, distributed source coding strategies are potentially beneficial. However, they require each BS to have information about the joint statistics of the received signals across the BSs, and they are generally sensitive to uncertainties regarding such information. Motivated by this observation, a robust compression method is proposed to cope with uncertainties on the correlation of the received signals. The problem is formulated using a deterministic worst case approach, and an algorithm is proposed that achieves a stationary point for the problem. Then, BS selection is addressed with the aim of reducing the number of active BSs, thus enhancing the energy efficiency of the network. An optimization problem is formulated in which compression and BS selection are performed jointly by introducing a sparsity-inducing term into the objective function. An iterative algorithm is proposed that is shown to converge to a locally optimal point. From numerical results, it is observed that the proposed robust compression scheme compensates for a large fraction of the performance loss induced by the imperfect statistical information. Moreover, the proposed BS selection algorithm is seen to perform close to the more complex exhaustive search solution.