Distributed Censored Regression Over Networks

Distributed estimation over sensor networks has received a lot of attention due to its great promise for broad applicability. In many cases, sensors have constraints on the range of data they can measure. This may cause that the measurements or observations are censored, and hence the value of a measurement or observation could be only partially known. This paper focuses on distributed censored regression over networks and develops a diffusion-based algorithm for the censored regression. The proposed algorithm first adopts an adaptive bias-corrected estimator based on a probit regression model to reduce the adverse effect of censoring on estimation results, and afterwards carries out the least squares procedure to find the estimate of the parameter of interest in a collaborative manner between every node and its neighbors. The theoretical study of convergence in the mean and mean-square sense reveals that the proposed algorithm is asymptotically unbiased and stable under some conditions. Moreover, simulation results show the effectiveness of the proposed algorithm.