An Adaptive-to-Model Test for Parametric Functional Single-Index Model

Model checking methods based on non-parametric estimation are widely used because of their tractable limiting null distributions and being sensitive to high-frequency oscillation alternative models. However, this kind test suffers from the curse dimensionality, resulting in slow convergence, especially for functional data with infinite dimensional features. In paper, we propose an adaptive-to-model a parametric single-index model by using orthogonality residual its conditional expectation. The achieves adaptation sufficient dimension reduction which utilizes sliced inverse regression. This procedure can be easily extended other methods. Under certain conditions, prove asymptotic properties statistic under hypothesis, fixed hypothesis local hypothesis. Simulations show that our has better performance than method does not use reduction. An analysis COVID-19 verifies conclusion.