For the reversible watermarking scheme using the prediction error expansion and histogram shifting (PEE-HS), improving the prediction accuracy facilitates performance enhancement, which still remains a challenging problem in this field. To this end, the paper improves the state-of-the-art local predictor (LP) by designing the following approaches: 1) enlarging the prediction context; 2) partitioning the prediction block surrounding the target pixel into the watermarked and original regions, and imposing different weights on prediction values from these two regions to generate the final prediction for the target pixel; and 3) conducting watermarking simulation on the original region via random noises to further enhance the prediction performance. These three approaches are then integrated to result in an improved LP using weighted prediction and watermarking simulation (LP-WPWS). By exploiting the LP-WPWS for prediction error generation, we thus construct a new PEE-HS-based reversible watermarking scheme. Extensive simulation shows that the proposed scheme outperforms the state-of-the-art LP and is comparable to the excellent methods exploiting the sorting, multiple histograms modification, and hybrid dimensional histogram generation with adaptive mapping selection.