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t 型回归估计量的崩溃点AI 解读

To bound the influence of a leverage point, generalised M-estimators have been suggested. However, the usual generalised M-estimator of regression has a breakdown point that is less than the inverse of its dimension. This paper shows that dimension-independent positive breakdown points can be attained by a class of well-defined generalised M-estimators with redescending scores. The solution can be determined through optimisation of t-type likelihood applied to properly…

杂录：样条变换后的线性回归AI 解读

In a transformation model h(Y) = X'β + ε for some smooth and usually monotone function h, we are often interested in the direction of β without knowing the exact form of h. We consider a projection of h onto a linear space of B-spline functions which has the highest correlation with the design variable X. As with the Box-Cox transformation, the transformed response may then be analysed by standard linear regression software. The direction estimate from canonical correlation…