Robust Asymptotic Statistics pp 261-330 | Cite as
Robust Regression
Chapter
Abstract
The linear regression model, with carriers treated random, has been defined through 2.4(36)–2.4(40):
By Theorem 2.4.6, the model is, at every θ∈ℝ k , L2 differentiable with L2 derivative and Fisher information of full rank given by
Thus the robustness results for general parameter apply with this ideal center model. Due to the regression structure, however, additional variants of neighborhoods, bias terms, and corresponding optimization (and, in principle, construction) problems arise.
$${P_\theta }(dx,dy) = f(y - x'\theta )\lambda (dy)K(dx),\theta \in {\mathbb{R}^k}$$
(1)
$${\Lambda _\theta }(x,y) = {\Lambda _f}(y - {\text{ }}x'\theta )x,{\text{ }}{I_f}K,{\text{ }}K{\text{ }} = {\text{ }}\int {xx'K(dx)} $$
(2)
Keywords
Robust Regression Influence Curve Conditional Bias Lagrangian Differentiation Tangent Subspace
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag New York, Inc. 1994