Resumen
This paper discusses asymptotic expansions for the null distributions of some test statistics for profile analysis under non-normality. It is known that the null distributions of these statistics converge to chi-square distribution under normality [Siotani, M., 1956. On the distributions of the Hotelling's T^2-statistics. Ann. Inst. Statist. Math. Tokyo 8, 1-14; Siotani, M., 1971. An asymptotic expansion of the non-null distributions of Hotelling's generalized T^2-statistic. Ann. Math. Statist. 42, 560-571]. We extend this result by obtaining asymptotic expansions under general distributions. Moreover, the effect of non-normality is also considered. In order to obtain all the results, we make use of matrix manipulations such as direct products and symmetric tensor, rather than usual elementwise tensor notation.