Tuning-Free Tests for Treatment Effect Heterogeneity via Expectile Processes

This paper develops tuning-free tests for treatment-effect heterogeneity. By characterizing the null hypothesis as constancy of the expectile treatment-effect curve, we construct test statistics as continuous functionals of the mean-centered sample expectile process. We establish a uniform Bahadur representation, derive the asymptotic properties of the test statistics under the null and fixed alternatives, and show nontrivial power against local alternatives approaching the null at the $n^{-1/2}$ rate. For feasible inference, we develop a fast multiplier bootstrap that consistently approximates the nonpivotal null distribution while capturing the first-order effect of estimating the unknown common shift. The procedure is tuning-free, requiring no density or score-function estimation, bandwidth selection, or repeated refitting. The framework further incorporates a pointwise-studentized refinement and a covariate adjustment that reduces asymptotic variation without altering the population discrepancy. Monte Carlo comparisons with existing methods show generally reliable size control, competitive power, and substantial computational savings. An application to a large-scale water-conservation experiment illustrates the proposed tests.