Introduces a Hilbert-valued one-step estimator for the kernel covariance operator between covariates and residuals that enables semiparametrically efficient inference on noise heterogeneity and residual independence in additive noise models.
A simpler condition for consistency of a kernel independence test
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abstract
A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has previously been shown that when the kernel used in defining the joint embedding is characteristic (that is, the embedding of the joint distribution to the feature space is injective), then the HSIC-based test is consistent. In particular, it is sufficient for the product of kernels on the individual domains to be characteristic on the joint domain. In this note, it is established via a result of Lyons (2013) that HSIC-based independence tests are consistent when kernels on the marginals are characteristic on their respective domains, even when the product of kernels is not characteristic on the joint domain.
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2026 1verdicts
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Semiparametrically Efficient Inference for Kernel Measures of Noise Heterogeneity
Introduces a Hilbert-valued one-step estimator for the kernel covariance operator between covariates and residuals that enables semiparametrically efficient inference on noise heterogeneity and residual independence in additive noise models.