A new dimension-reduction graphical method for testing high- dimensional normality is developed by using the theory of spherical distributions and the idea of principal component analysis. The dimension reduction is r...A new dimension-reduction graphical method for testing high- dimensional normality is developed by using the theory of spherical distributions and the idea of principal component analysis. The dimension reduction is realized by projecting high-dimensional data onto some selected eigenvector directions. The asymptotic statistical independence of the plotting functions on the selected eigenvector directions provides the principle for the new plot. A departure from multivariate normality of the raw data could be captured by at least one plot on the selected eigenvector direction. Acceptance regions associated with the plots are provided to enhance interpretability of the plots. Monte Carlo studies and an illustrative example show that the proposed graphical method has competitive power performance and improves the existing graphical method significantly in testing high-dimensional normality.展开更多
We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on rev...We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.展开更多
文摘A new dimension-reduction graphical method for testing high- dimensional normality is developed by using the theory of spherical distributions and the idea of principal component analysis. The dimension reduction is realized by projecting high-dimensional data onto some selected eigenvector directions. The asymptotic statistical independence of the plotting functions on the selected eigenvector directions provides the principle for the new plot. A departure from multivariate normality of the raw data could be captured by at least one plot on the selected eigenvector direction. Acceptance regions associated with the plots are provided to enhance interpretability of the plots. Monte Carlo studies and an illustrative example show that the proposed graphical method has competitive power performance and improves the existing graphical method significantly in testing high-dimensional normality.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301063 and 11571067)Science and Technology Development Foundation of Jilin (Grant No. 20160520174JH)Science and Technology Foundation of Jilin during the "13th Five-Year Plan"
文摘We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.