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Globally robust inference for simple linear regression models with repeated median slope estimator Khan, Md Jafar Ahmed


Globally robust inference takes into account the potential bias of the point estimates (Adrover, Salibian-Barrera and Zamar, 2002). To construct robust confidence intervals for the simple linear regression slope, the authors selected the generalized median of slopes (GMS) as their point estimate, considering its good bias behavior and asymptotic normality. However, GMS has a breakdown point of only 0.25, its asymptotic normality is established under very restrictive conditions, and its bias bound is known only for symmetric carrier distributions. In this study, we propose the repeated median slope (RMS) estimate as an alternative choice. RMS has a breakdown point of 0.50, its asymptotic normality holds under mild assumptions, and the bias bound for RMS is known for general carrier distributions. The proposed method achieves, more or less, the same observed coverage levels while it constructs intervals of smaller lengths, as compared to the GMS approach.

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