Censored Regression With Noisy Input

There has been a great deal of interest in estimating parameters of the censored regression model, which arises in a regular regression situation if the measuring device fails to give a true measurement above or below a given level. Most previous works however are based on the assumption that the regressor (system input) is noise-free, which is not always true in many practical applications. In this paper, we focus on estimating parameters of a more general censored regression model which allows the regressor as well as the response to be observed with noises. In this case, ordinary least-squares estimators suffer from serious biases, which result from the censored outputs and noisy inputs as well. In order to solve the problem, we develop an efficient bias-compensated Heckman algorithm (BC-Heckman) for censored regression with noisy input. The BC-Heckman is able to significantly reduce the biases and thus outperforms the previously proposed algorithms. In addition, we also extend the algorithm to the distributed scenario where the data is distributed over many sensor nodes forming a network. The theoretical analysis results show the BC-Heckman algorithms have good convergence and steady state behaviors, and simulation experiments further demonstrate the good performance.