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In this paper,distributed regression estimation problem with incomplete data in a time-varying multi-agent network is investigated.Regression estimation is carried out based on local agent information with incomplete in the non-ignorable mechanism.By virtue of gradient-based design and adaptive filter,a distributed algorithm is proposed to deal with a regression estimation problem with incomplete data.With the help of convex analysis and stochastic approximation techniques,the exact convergence is obtained for the proposed algorithm with incomplete data and a jointly-connected multi-agent topology.Moreover,online regret analysis is also given for real-time leaing.Then,simulations for the proposed algorithm are also given to demonstrate how it can solve the estimation problem in a distributed way,even when the network configuration is time-varying.