论文标题
通过简化的平滑回合估算的添加模型的非参数推断
Nonparametric inference for additive models estimated via simplified smooth backfitting
论文作者
论文摘要
我们研究了使用简化的平滑背贴估计的非参数添加剂模型中的假设检验（Huang和Yu，《计算和图形统计杂志》，\ TextBf {28（2）}，386---400，2019）。简化的平滑背贴在规律性条件下实现了甲骨文特性，并提供了估计器的封闭形式表达式，这些表达式可用于推导渐近性能。我们开发了广义的似然比（GLR）和基于推理的基于损耗函数（LF）的测试框架。在零假设下，GLR和LF检验均具有渐近缩放的卡方分布，并且都表现出Wilks现象，这意味着缩放常数和自由度与滋扰参数无关。这些测试在非参数假设检验的收敛速率方面渐近最佳。另外，适合模型估计的带宽可能对测试很有用。我们表明，在加性模型中，LF测试在渐近上比GLR测试更强大。我们使用模拟来证明Wilks现象以及这些提出的GLR和LF测试的功能，以及一个真正的例子来说明它们的实用性。
We investigate hypothesis testing in nonparametric additive models estimated using simplified smooth backfitting (Huang and Yu, Journal of Computational and Graphical Statistics, \textbf{28(2)}, 386--400, 2019). Simplified smooth backfitting achieves oracle properties under regularity conditions and provides closed-form expressions of the estimators that are useful for deriving asymptotic properties. We develop a generalized likelihood ratio (GLR) and a loss function (LF) based testing framework for inference. Under the null hypothesis, both the GLR and LF tests have asymptotically rescaled chi-squared distributions, and both exhibit the Wilks phenomenon, which means the scaling constants and degrees of freedom are independent of nuisance parameters. These tests are asymptotically optimal in terms of rates of convergence for nonparametric hypothesis testing. Additionally, the bandwidths that are well-suited for model estimation may be useful for testing. We show that in additive models, the LF test is asymptotically more powerful than the GLR test. We use simulations to demonstrate the Wilks phenomenon and the power of these proposed GLR and LF tests, and a real example to illustrate their usefulness.
