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最小修剪差分回归估计量及其替代方法AI 解读

This article proposes and studies the performance in theory and practice of the least trimmed differences (LTD) linear regression estimator. The estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals. We obtain the breakdown point, maxbias curve, and large-sample properties of a class of estimators including the LTD as special case. The LTD estimator has a 50% breakdown point and Gaussian efficiency of…

最小截尾差分回归估计量及其替代方法AI 解读

This article proposes and studies the performance in theory and practice of the least trimmed differences (LTD) linear regression estimator. The estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals. We obtain the breakdown point, maxbias curve, and large-sample properties of a class of estimators including the LTD as special case. The LTD estimator has a 50% breakdown point and Gaussian efficiency of…

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高崩溃点非线性回归参数的计算AI 解读

Most algorithms for estimating high breakdown regression estimators in linear regression rely on finding the least squares fit to many p-point elemental sets, where p is the dimension of the X matrix. Such an approach is computationally infeasible in nonlinear regression. This article presents a new algorithm for computing high breakdown estimates in nonlinear regression that requires only a small number of least squares fits to p points. The algorithm is used to compute…

非线性回归中的击穿AI 解读

The breakdown point is considered an important measure of the robustness of a linear regression estimator. This article addresses the concept of breakdown in nonlinear regression. Because it is not invariant to nonlinear reparameterization, the usual definition of the breakdown point in linear regression is inadequate for nonlinear regression. The original definition of breakdown due to Hampel is more suitable for nonlinear problems but may indicate breakdown when the fitted…