We extend the rate distortion theory of motion-compensated prediction to linear predictive models. The power spectrum of the motion-compensated prediction error is related to the displacement error pdfs of an arbitrary number of linear predictor input signals in a closed form expression. The influence of the residual noise level and the gains achievable are investigated. We then extend the scalar approach to motion-compensated vector prediction. The vector predictor coefficients are fixed, but we conduct a search to find the optimum input vectors. We control the rate of the motion compensation data which have to be transmitted as side information to the decoder by minimizing a Lagrangian cost function where the regularization term is given by the entropy associated with the motion compensation data. An adaptive algorithm for optimally selecting the size of the linear vector predictor is given. The designed motion-compensated vector predictors show PSNR gains up to 4.4 dB at the cost of increased bit-rate of 16 kbit/s when comparing them to conventional motion-compensated prediction.