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Accurate end-to-end distortion estimation is critical to efficient rate-distortion (R-D) optimization of encoder decisions for video transmission over lossy packet networks. This work focuses on extensions of the recursive optimal per-pixel estimate (ROPE), which has been shown to provide accurate end-to-end distortion estimation. Of particular interest are difficulties due to sub-pixel prediction and other pixel averaging operations, for which the existing ROPE encounters cross-correlation terms, whose exact estimation requires prohibitive storage and computational complexity. In this paper, we propose two model-based methods, which approximate the cross-correlation of two pixels as a function of their available first and second marginal moments. This allows an approximate extension of ROPE to handle sub-pixel prediction and other pixel averaging operations, at no additional storage cost, and no significant additional complexity. Simulations provide evidence for the performance gains of the proposed methods, and in particular, demonstrate that the resulting accuracy is very close to that of ROPE when it is optimal, i.e., in the case of full pixel prediction.