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- W2023278697 abstract "Consider the linear regression model y=β01 +Xβ+ in the usual notation. It is argued that the class of ordinary ridge estimators obtained by shrinking the least squares estimator by the matrix (X1X + kI)-1X'X is sensitive to outliers in the ^variable. To overcome this problem, we propose a new class of ridge-type M-estimators, obtained by shrinking an M-estimator (instead of the least squares estimator) by the same matrix. Since the optimal value of the ridge parameter k is unknown, we suggest a procedure for choosing it adaptively. In a reasonably large scale simulation study with a particular M-estimator, we found that if the conditions are such that the M-estimator is more efficient than the least squares estimator then the corresponding ridge-type M-estimator proposed here is better, in terms of a Mean Squared Error criteria, than the ordinary ridge estimator with k chosen suitably. An example illustrates that the estimators proposed here are less sensitive to outliers in the y-variable than ordinary ridge estimators." @default.
- W2023278697 created "2016-06-24" @default.
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- W2023278697 date "1991-09-01" @default.
- W2023278697 modified "2023-10-02" @default.
- W2023278697 title "ROBUST RIDGE REGRESSION BASED ON AN M-ESTIMATOR" @default.
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- W2023278697 doi "https://doi.org/10.1111/j.1467-842x.1991.tb00438.x" @default.
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