Erasure entropy rate (introduced recently by Verdú and Weissman) differs from Shannon's entropy rate in that the conditioning occurs with respect to both the past and the future, as opposed to only the past (or the future). In this paper, universal algorithms for estimating erasure entropy rate are proposed based on the basic and extended context-tree weighting (CTW) algorithms. Consistency results are shown for those CTW based algorithms. Simulation results for those algorithms applied to Markov sources, tree sources and English texts are compared to those obtained by fixed-order plug-in estimators with different orders. An estimate of the erasure entropy of English texts based on the proposed algorithms is about 0.22 bits per letter, which can be compared to an estimate of about 1.3 bits per letter for the entropy rate of English texts by a similar CTW based algorithm.