DeBiased TwoSample UStatistics With Application To Conditional Distribution Testing
Abstract
In some highdimensional and semiparametric inference problems involving two populations, the parameter of interest can be characterized by twosample Ustatistics involving some nuisance parameters. In this work we first extend the framework of onestep estimation with crossfitting to twosample Ustatistics, showing that using an orthogonalized influence function can effectively remove the first order bias, resulting in asymptotically normal estimates of the parameter of interest. As an example, we apply this method and theory to the problem of testing twosample conditional distributions, also known as strong ignorability. When combined with a conformalbased ranksum test, we discover that the nuisance parameters can be divided into two categories, where in one category the nuisance estimation accuracy does not affect the testing validity, whereas in the other the nuisance estimation accuracy must satisfy the usual requirement for the test to be valid. We believe these findings provide further insights into and enhance the conformal inference toolbox.
 Publication:

arXiv eprints
 Pub Date:
 January 2024
 DOI:
 10.48550/arXiv.2402.00164
 arXiv:
 arXiv:2402.00164
 Bibcode:
 2024arXiv240200164C
 Keywords:

 Statistics  Methodology
 EPrint:
 25 pages, 1 figure, 6 tables