Hypothesis testing concerning location vectors is one of the fundamental problems in multivariate statistical analysis. The classical Hotelling T^2 (HT) test is a powerful tool for testing the location vectors and has many superiorities. However, the HT test is no longer valid when the dimension p is greater than or equal to the sample size n due to the non-invertibility of the sample covariance matrix. Even when p<n, it will also lose its power if p is close to n. HT test statistic is a function of likelihood ratio statistic, which is obtained under the condition that samples are generated from normal distribution. When samples are not normal distributed, the sample mean and sample covariance matrix are not independent, so that it is difficult to obtain asymptotically normal theory of HT test. We correct the HT test by the fourth moment theorem in the large dimensional framework, and obtain the Ridgelized Hotelling’s T^2 (RIHT) test method. It is worth to mention that our study includes one-sample mean vector test, testing the equality of several mean vectors under homoskedasticity, and testing the two-sample problem that under heteroscedasticity. In our study, we do not require that the samples are from the normal distribution. We prove the asymptotic normality of the RIHT test statistics under the condition that the underlying distribution is arbitrary. The estimations of the asymptotic mean and asymptotic variance are also presented in the current paper and the in the presentation.