We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models based on the cross-validation and allows for heteroscedasticity of the errors of models. We develop its asymptotic distributions for comparing additive models and varying-coefficient models and extend it to test significance of variables in additive models with massive data. The method is applicable to model selection among supervised learning models. To facilitate implementation of the test, we provide a fast calculation procedure. Simulations show that the proposed tests work well and have favorable finite sample performance over some existing approaches. The methodology is validated on an empirical application.
翻译:我们建议对非参数模型选择进行实证概率比率测试,使相互竞争的模型可以嵌套、不赦免、重叠、错误指定或正确指定,比较基于交叉校验的模型的方形预测错误,并允许模型误差的异异性。我们开发其无症状分布,用于比较添加模型和不同效益模型,并将它扩大到测试具有大量数据的添加模型中的变量的重要性。这种方法适用于受监督学习模型的模型选择。为了便利测试的实施,我们提供了一个快速计算程序。模拟显示,拟议的测试效果良好,对一些现有方法具有有利的有限抽样性。该方法在经验应用中验证。