High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound

This paper deals with the null distribution of a likelihood ratio (LR) statistic for testing the intraclass correlation structure. We derive an asymptotic expansion of the null distribution of the LR statistic when the number of variable p and the sample size N approach infinity together, while the ratio p / N is converging on a finite nonzero limit c ∈ ( 0 , 1 ) . Numerical simulations reveal that our approximation is more accurate than the classical χ 2 -type and F -type approximations as p increases in value. Furthermore, we derive a computable error bound for its asymptotic expansion.