The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LT...The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.展开更多
为使原始LTS(least trimm ed squares)方法能够处理非线性问题,研究非线性LTS稳健估计方法。说明该方法的解一定是部分观测值的非线性最小二乘估计。该方法可通过求解非线性最小二乘问题得到确切解。基于MM EA(m in im um m ax im um ex...为使原始LTS(least trimm ed squares)方法能够处理非线性问题,研究非线性LTS稳健估计方法。说明该方法的解一定是部分观测值的非线性最小二乘估计。该方法可通过求解非线性最小二乘问题得到确切解。基于MM EA(m in im um m ax im um exchange a lgorithm)算法和非线性最小二乘技术,构建求解非线性LTS估计近似解的算法。仿真结果表明非线性LTS估计方法能够同时抵抗来自X方向和Y方向的多个异常,与传统方法相比具有更好的稳健性。展开更多
文摘The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.
文摘为使原始LTS(least trimm ed squares)方法能够处理非线性问题,研究非线性LTS稳健估计方法。说明该方法的解一定是部分观测值的非线性最小二乘估计。该方法可通过求解非线性最小二乘问题得到确切解。基于MM EA(m in im um m ax im um exchange a lgorithm)算法和非线性最小二乘技术,构建求解非线性LTS估计近似解的算法。仿真结果表明非线性LTS估计方法能够同时抵抗来自X方向和Y方向的多个异常,与传统方法相比具有更好的稳健性。
