We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encompassing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth's choice. We investigate two alternative approaches to obtain a "small bias property" for our test statistics. We show the validity of a wild bootstrap method. We empirically study the use of a data-driven bandwidth and illustrate the attractive features of our tests for small and moderate samples.

翻译：我们通过L2距离建立了一个形式化框架，用以刻画非参数模型的包容性特征。将其与非参数回归模型比较领域的既有文献进行对比后，我们发展了完全非参数化的包容性假设检验程序。检验统计量依赖于核回归方法，由此引发带宽选择问题。我们研究了两种替代方法以确保检验统计量具备"小偏倚性质"，并验证了野自助法（wild bootstrap）的有效性。通过实证研究数据驱动型带宽的应用，我们揭示了该检验在小样本与中等样本情况下所具备的优良特性。