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 pp and the sample size NN approach infinity together, while the ratio p/Np/N is converging on a finite nonzero limit c∈(0,1)c∈(0,1). Numerical simulations reveal that our approximation is more accurate than the classical χ2χ2-type and FF-type approximations as pp increases in value. Furthermore, we derive a computable error bound for its asymptotic expansion.