Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications.In this paper,we propose a new test statistic based on the Frobenius norm and subt...Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications.In this paper,we propose a new test statistic based on the Frobenius norm and subtracting bias technique,which is generally applicable to high-dimensional data without restricting the distributional Assumptions.The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation.Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions.To make the test statistic applicable,we introduce a wild bootstrap method and demonstrate its validity.The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests,even when the normal approximation is invalid.Real data analysis is devoted to illustrating the proposed test.展开更多
Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of in...Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.12271370 and 12371294)the Youth Academic Innovation Team Construction project of the Capital University of Economics and Business(Grant No.QNTD202303)New Young Teachers’Research Initiation Fund Project,Capital University of Economics and Business(Grant No.XRZ2021046)。
文摘Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications.In this paper,we propose a new test statistic based on the Frobenius norm and subtracting bias technique,which is generally applicable to high-dimensional data without restricting the distributional Assumptions.The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation.Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions.To make the test statistic applicable,we introduce a wild bootstrap method and demonstrate its validity.The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests,even when the normal approximation is invalid.Real data analysis is devoted to illustrating the proposed test.
基金partially supported by Beijing Natural Science Foundation under Grant No.Z180006.
文摘Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.
