 Asymptotic normality of support vector machine variants and other regularized kernel methodsRobert Hable Journal of Multivariate Analysis, 2012, vol. 106, issue C, 92-117 Abstract: In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods (simply called SVMs here) can be seen as regularized M-estimators for a parameter in a (typically infinite dimensional) reproducing kernel Hilbert space. For smooth loss functions L, it is shown that the difference between the estimator, i.e. the empirical SVM fL,Dn,λDn, and the theoretical SVM fL,P,λ0 is asymptotically normal with rate n. That is, n(fL,Dn,λDn−fL,P,λ0) converges weakly to a Gaussian process in the reproducing kernel Hilbert space. As common in real applications, the choice of the regularization parameter Dn in fL,Dn,λDn may depend on the data. The proof is done by an application of the functional delta-method and by showing that the SVM-functional P↦fL,P,λ is suitably Hadamard-differentiable. Keywords: Nonparametric regression; Support vector machine; Regularized kernel method; Asymptotic normality; Hadamard-differentiability; Functional delta-method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:106:y:2012:i:c:p:92-117 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2011.11.004 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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