Considering that perfect channel state information (CSI) is difficult to obtain in practice, energy efficiency (EE) for distributed antenna systems (DAS) based on imperfect CSI and antennas selection is investigated in Rayleigh fading channel. A novel EE that is defined as the average transmission rate divided by the total consumed power is introduced. In accordance with this definition, an adaptive power allocation (PA) scheme for DAS is proposed to maximize the EE under the maximum transmit power constraint. The solution of PA in the constrained EE optimization does exist and is unique. A practical iterative algorithm with Newton method is presented to obtain the solution of PA. The proposed scheme includes the one under perfect CSI as a special case, and it only needs large scale and statistical information. As a result, the scheme has low overhead and good robustness. The theoretical EE is also derived for performance evaluation, and simulation result shows the validity of the theoretical analysis. Moreover, EE can be enhanced by decreasing the estimation error and/ or path loss exponents.