部分函数型线性模型中高维回归系数的检验

Test for High-Dimensional Regression Coeffcients in Partially Functional Linear Models

  • 摘要: 在实际应用中常常会遇到高维和函数型数据的混合数据. 部分函数型线性模型是处理这种混合型数据的有力工具. 本文基于部分函数型线性模型构造 U 检验统计量, 讨论模型中高维回归系数的全局检验问题. 应用鞅的中心极限定理, 证明了所提出检验统计量在原假设和局部备择下的渐近分布.通过蒙特卡洛数值模拟验证了该检验统计量在有限样本情形下具有良好水平和功效. 最后, 将该方法应用于环境污染数据, 展示了其有效性和实用性.

     

    Abstract: In practical application, functional and high-dimensional data are often observed simultaneously. The partially functional linear model is a powerful tool for handling this type of mixed data. In this paper, we develop a U test statistic to discuss the overall test for high-dimensional regression coeffcients in partially functional linear models. With the aid of the martingale central limit theorem, we prove the asymptotic distributions of the proposed test under the null hypothesis and local alternative hypothesis. We examine the finite-sample performances of the proposed test via Monte Carlo simulations, which show that the new test works well both in size and power. We also demonstrate the effectiveness and application by an empirical analysis of a air pollution data set.

     

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