Model checking for parametric single-index models with massive datasets

Model checking is essential for making reliable statistical inferences. For massive datasets, we develop a new distributed method for testing parametric single-index models by integrating the divide and conquer strategy into the dimension reduction model-adaptive (DRMA) test. A distributed method for the determination of the struc-tural dimension is also proposed. The asymptotic behaviors of the proposed test statistic under the null and alternative model are derived, which shows that the proposed test has the same limiting behavior of the DRMA test based on the entire dataset. In addition, the proposed test achieves adaptive rate-optimality using the sample-splitting strategy for selecting bandwidth. Our simulation results and a data illustration demonstrate that the proposed test performs better than the existing tests for massive datasets, especially when the dimension of covariates is large.(c) 2023 Elsevier B.V. All rights reserved.