Cross-Validated Kernel Ensemble: Robust Hypothesis Test for Nonlinear Effect with Gaussian Process.

The R package CVEK introduces a robust hypothesis test for nonlinear effect with Gaussian process. CVEK is an ensemble-based estimator that adaptively learns the form of the main-effect kernel from data, and constructs an companion variance component test. Package CVEK implements the estimator for two testing procedures, namely asymptotic test and bootstrap test. Additionally, it implements a variety of tuning parameter criteria, including Akaike Information Criteria, Generalized Cross Validation, Generalized Maximum Profile Marginal Likelihood and leave-one-out Cross Validation. Moreover, there are three kinds of ensemble strategies to create the ultimate ensemble kernel: Simple Averaging, Empirical Risk Minimization and Exponential Weighting. The null distribution of the test statistic can be approximated using a scaled chi-square distribution, and therefore statistical inference based on the results of this package, such as hypothesis testing can be performed. Extensive simulations demonstrate the robustness and correct implementation of the estimator.