广义线性模型的模型检验：一种降维模型自适应方法
Model checking for generalized linear models: a dimension-reduction model-adaptive approach
摘要：
基于多元非参数回归估计的局部平滑检验是目前文献中主要的模型检验方法之一。然而，相关的测试遭受从典型的灾难的维数导致缓慢的收敛速度到他们的极限下的零假设和较小的偏差下的替代品。这个问题导致测试不能很好地保持显著性水平，并且对替代方案不太敏感。本文提出了一种针对广义线性模型的降维模型自适应检验方法。该测试表现得像一个局部平滑测试，就好像模型是单变量的，并且可以与任何全局替代品保持一致，并且可以以快速的速度检测不同于空值的局部替代品，现有的局部平滑测试只有在模型是单变量时才能实现。仿真进行了检查我们的方法的性能。最后以一个实际数据进行了分析。该方法可以推广到全局平滑方法和其它测试问题。
英文摘要：
Local smoothing testing that is based on multivariate nonparametric regression estimation is one of the main model checking methodologies in the literature. However, relevant tests suffer from the typical curse of dimensionality resulting in slow convergence rates to their limits under the null hypotheses and less deviation from the null under alternatives. This problem leads tests to not well maintain the significance level and to be less sensitive to alternatives. In this paper, a dimension-reduction model-adaptive test is proposed for generalized linear models. The test behaves like a local smoothing test as if the model were univariate, and can be consistent against any global alternatives and can detect local alternatives distinct from the null at a fast rate that existing local smoothing tests can achieve only when the model is univariate. Simulations are carried out to examine the performance of our methodology. A real data analysis is conducted for illustration. The method can readily be extended to global smoothing methodology and other testing problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
