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首页> 外文期刊>IEEE Transactions on Signal Processing >Recursive Least Squares for Censored Regression
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Recursive Least Squares for Censored Regression

机译：递归最小二乘删失回归

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摘要

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.
机译：在许多工程任务中自然会遇到经过审查的观测结果。当对观察结果进行不合要求的审查时，常规的估计算法可能会遭受性能的显着下降。这项工作的重点是自适应地估计审查回归（CR）模型中的回归参数。我们首先认为噪声方差和删失阈值是先验已知的，并且通过在期望最大化框架中计算最大似然估计来解决在线CR问题。该策略产生了CR的递归最小二乘算法（CR-RLS），我们证明了其收敛性，并给出了稳态误差的分析结果。接下来，我们将CR-RLS扩展到未知噪声方差和审查阈值的情况。理论分析和数值模拟表明，在估计精度和收敛速度方面，CR-RLS的性能均明显优于其他竞争算法。特别是，对于不同的审查阈值，CR-RLS始终可以实现良好的性能，其稳态解几乎与具有未经审查（完整）观测值的RLS算法的精确度一样。

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