Adaptive-to-Model Hybrid of Tests for Regressions

In model checking for regressions, nonparametric estimation-based tests usually have tractable limiting null distributions and are sensitive to oscillating alternative models, but suffer from the curse of dimensionality. contrast, empirical process-based can, at fastest possible rate, detect local alternatives distinct model, yet less rely on Monte Carlo approximation critical value determination, which is costly in computation. We propose an adaptive-to-model hybrid moment conditional moment-based fully inherit merits these two types avoid shortcomings. Further, such a makes tests, under alternatives, also share existing tests. The methodology can be readily applied other kinds data construction hybrids. As by-product sufficient dimension reduction field, study residual-related central mean subspace adaptation devoted showing when models indicated cannot. Numerical studies conducted verify powerfulness proposed test.