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

In this paper, the asymptotical properties on the likelihood ratio test in high-dimensional exploratory factor analysis are considered. When the dimension of the response variable p satisfies p = p(N) → ∞ and p/N → c ∈ (0, 1) as the sample size N → ∞, 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.