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For big data arriving in streams online updating is an important statistical method that breaks the storage barrier and the computational barrier under certain circumstances. In the regression context online updating algorithms assume that the set of predictor variables does not change, and consequently cannot incorporate new variables that may become available midway through the data stream. A naive approach would be to discard all previous information and start updating with new variables from scratch. We propose a method that utilizes the information from earlier data in the online updating algorithm with bias corrections to improve efficiency. The method is developed for linear models first, and then extended to estimating equations for generalized linear models. Closed‐form expressions for the efficiency gain over the naive approach are derived in a particular linear model setting. We compare the …