Mediation analysis draws increasing attention in many scientific areas such as genomics, epidemiology and finance. In this paper, we propose new statistical inference procedures for high dimensional mediation models, in which both the outcome model and the mediator model are linear with high dimensional mediators. Traditional procedures for mediation analysis cannot be used to make statistical inference for high dimensional linear mediation models due to high-dimensionality of the mediators. We propose an estimation procedure for the indirect effects of the models via a partial penalized least squares method, and further establish its theoretical properties. We further develop a partial penalized Wald test on the indirect effects, and prove that the proposed test has a $\chi^2$ limiting null distribution. We also propose an $F$-type test for direct effects and show that the proposed test asymptotically follows a $\chi^2$-distribution under null hypothesis and a noncentral $\chi^2$-distribution under local alternatives. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed tests and compare their performance with existing ones. We further apply the newly proposed statistical inference procedures to study stock reaction to COVID-19 pandemic via an empirical analysis of studying the mediation effects of financial metrics that bridge company's sector and stock return.
翻译:在本文件中,我们为高维调解模式提出了新的统计推论程序,其中结果模型和调解员模型都与高维调解人相直线,传统的调解分析程序不能用于对高维线调解模型进行统计推论,因为调解人具有高维性,因此调解分析的传统程序不能用来对高维线调解模型进行统计推论,我们建议了通过部分惩罚性最低方的方法对这些模型的间接影响进行估算程序,并进一步确立了其理论属性。我们进一步制定了对间接影响的部分惩罚性沃尔德测试,并证明拟议的测试有1 chi2美元限制无效分布。我们还提出了对直接影响的F$型测试,并表明拟议的测试在完全假设和当地替代品下非中央分配$1 chi2美元之后进行。我们进行了蒙特卡洛模拟,以审查拟议测试的有限样品性能,并将其绩效与现有测试进行比较。我们还进一步采用了新提议的统计推论程序,以研究通过CVI-19号公司大宗大宗大宗大宗大案的金融影响和大宗大宗大宗大宗的金融影响分析的股票反应,通过CSurvial Regisal Res重回公司-Cal 的金融影响分析。