On the asymptotic of likelihood ratio statistic in high-dimensional exploratory factor analysis

Abstract

In this paper, the asymptotical properties on the likelihood ratio  test in high-dimensional exploratory factor analysis is considered. When the dimension of the response variable  and the sample size tend to infinity with the same rate,  the Edgeworth expansion of the null distribution of the likelihood ratio test statistic and its uniform  error  bound are established. Some numerical simulations indicate that the proposed approximation is more accurate than the traditional chi-square approximate method on dealing with the high-dimensional test.