Recursive Least Squares for Censored Regression

Censored observations are encountered naturally in many engineering tasks. Conventional estimation algorithms may suffer from significant performance degradation when the observations are undesirably censored. This work focuses on adaptively estimating the regression parameter in a censored regression (CR) model. We first consider that the noise variance and censored thresholds are known a priori, and solve the online CR problem by computing the maximum-likelihood estimate in an expectation-maximization framework. This strategy yields a recursive least-squares algorithm for the CR (CR-RLS), and we prove its convergence and present analytical results for the steady-state error. Next, we extend the CR-RLS to the case of unknown noise variance and censored thresholds. Theoretical analysis and numerical simulation indicate that the CR-RLS performs significantly better than other competing algorithms in terms of both the estimation accuracy and convergence rate. Especially, for different censored thresholds, the CR-RLS can always achieve good performance, and its steady-state solution is almost as accurate as that of the RLS algorithm with the uncensored (complete) observations.