Neighborhoods as Nuisance Parameters? Robustness vs. Semiparametrics

Neighborhoods as Nuisance Parameters

Deviations from the center within a robust neighborhood may naturally be considered an innnite dimensional nuisance parameter. Thus, in principle, the semiparametric method may be tried, which is to compute the scores function for the main parameter minus its orthogonal projection on the closed linear tangent space for the nuisance parameter, and then rescale for Fisher consistency. We derive s...

Neighborhoods as Nuisance

Fawzi, Frossard: Measuring the Effect of Nuisance Variables

In real-world classification problems, nuisance variables can cause wild variability in the data. Nuisance corresponds for example to geometric distortions of the image, occlusions, illumination changes or any other deformations that do not alter the ground truth label of the image. It is therefore crucial that designed classifiers are robust to nuisance variables, especially when these are dep...

Orthogonal Machine Learning: Power and Limitations

Double machine learning provides √ n-consistent estimates of parameters of interest even when highdimensional or nonparametric nuisance parameters are estimated at an n−1/4 rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters. We show that the n−1/4 requirement can be improved to n−1/(2k+2) by employing a kth...

Improving the Efficiency of the Log-rank Test Using Auxiliary Covariates

Under the assumption of proportional hazards, the log-rank test is optimal for testing the null hypothesis of H0 : β = 0, where β denotes the logarithm of the hazard ratio. However, if there are additional covariates that correlate with survival times, making use of their information will increase the efficiency of the log-rank test. We apply the theory of semiparametrics to characterize a clas...