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An Omnibus Nonparametric Test Of Equality In Distribution For Unknown Functions, Alexander Luedtke, Marco Carone, Mark Van Der Laan
An Omnibus Nonparametric Test Of Equality In Distribution For Unknown Functions, Alexander Luedtke, Marco Carone, Mark Van Der Laan
Alex Luedtke
We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], using recent developments from the higher-order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed rather simply as U-statistics. We study the asymptotic behavior of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests …
Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke
Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke
Alex Luedtke
Frangakis et al. (2015) proposed a numerical method for computing the efficient influence function of a parameter in a nonparametric model at a specified distribution and observation (provided such an influence function exists). Their approach is based on the assumption that the efficient influence function is given by the directional derivative of the target parameter mapping in the direction of a perturbation of the data distribution defined as the convex line from the data distribution to a pointmass at the observation. In our discussion paper Luedtke et al. (2015) we propose a regularization of this procedure and establish the validity …