A Two-Step Projection-Based Goodness-of-Fit Test for Ultra-High Dimensional Sparse Regressions
超高维稀疏回归的两步投影拟合优度检验
This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders existing goodness-of-fit tests for regressions infeasible, primarily due to the curse of dimensionality or their reliance on the asymptotic linearity and normality of parameter estimators -- properties that may no longer hold under…