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Title: Non-parametric hypothesis testing with a nuisance parameter: A permutation test approach Authors:  EunYi Chung - University of Illinois at Urbana Champaign (United States) [presenting]
Abstract: A classical problem in statistics is studied: testing goodness of fit in the presence of a nuisance parameter. The main contribution is a novel permutation test for this testing problem that is asymptotically valid under fairly weak assumptions, while still providing an exact error control in finite samples under more restrictive conditions. In addition, the permutation test presented has finite- and large-sample properties comparable to those existing in the literature. The main result relies on the martingale transformation of the empirical process previously introduced. A noteworthy application of this testing problem is the one of testing for heterogeneous treatment effect in a randomized experiment. In this context, the null hypothesis implies that the distribution of the treatment and control groups are a constant shift apart. Moreover, the proposed method can be extended to testing the joint null hypothesis that treatment effects are constant within individual subgroups, while allowing for varying average treatment effects across subgroups. As a result, this test is able to detect treatment effect heterogeneity within individual subgroups even if the average treatment effects are identical across subgroups.