论文标题
功能线性模型的自适应模型检查测试
An adaptive model checking test for functional linear model
论文作者
论文摘要
许多研究专门用于功能线性模型(FLM)的估计和推理问题。但是,很少有工作重点放在模型检查问题上,以确保结果的可靠性。该领域的有限测试在替代方案下没有可进行的无效分布或渐近分析。同样,通常认为功能预测变量是完全观察到的,这是不切实际的。为了解决这些问题,我们提出了FLM的自适应模型检查测试。它结合了常规的基于力矩和条件力矩测试,并通过基于残差的子空间的维度实现模型适应性。我们测试的优势是多种多样的。首先,与其组件相比,它具有可拖动的卡方空分布和更高的替代功率。其次,开发了不同基础模型下的渐近特性,包括未访问的局部替代方案。第三,测试统计量是在有限的网格点上构建的,其中包含收集数据的离散性质。我们发展了样本量与网格点数量之间的理想关系,以维持渐近性能。此外,我们提供了一种数据驱动的方法来估计导致模型适应性的维度,这在足够的尺寸降低中有望。我们进行全面的数值实验,以证明测试从其两个简单组件中继承的优势。
Numerous studies have been devoted to the estimation and inference problems for functional linear models (FLM). However, few works focus on model checking problem that ensures the reliability of results. Limited tests in this area do not have tractable null distributions or asymptotic analysis under alternatives. Also, the functional predictor is usually assumed to be fully observed, which is impractical. To address these problems, we propose an adaptive model checking test for FLM. It combines regular moment-based and conditional moment-based tests, and achieves model adaptivity via the dimension of a residual-based subspace. The advantages of our test are manifold. First, it has a tractable chi-squared null distribution and higher powers under the alternatives than its components. Second, asymptotic properties under different underlying models are developed, including the unvisited local alternatives. Third, the test statistic is constructed upon finite grid points, which incorporates the discrete nature of collected data. We develop the desirable relationship between sample size and number of grid points to maintain the asymptotic properties. Besides, we provide a data-driven approach to estimate the dimension leading to model adaptivity, which is promising in sufficient dimension reduction. We conduct comprehensive numerical experiments to demonstrate the advantages the test inherits from its two simple components.