High-dimensional data, where the number of variables p is large compared to the sample size n, are widely available from microarray studies, finance and many other sources. This dissertation focuses on the effects of high dimensionality on some aspects of statistical inference. A two-sample test for means of high-dimensional data

proposed in this dissertation allows p to be much larger than n. We will show that in the simulation study the proposed test statistic performed consistently better than the other existing methods. Two distributions sharing the same mean may differ in many other aspects. We therefore consider a two-sample test for high-dimensional distributions. The proposed test statistic is based on empirical distribution functions

and is a natural extension to our two-sample test statistic for means. Empirical likelihood has many important applications in nonparametric or semiparametric statistical inference. In this dissertation, we further study the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high-dimensional data under a general multivariate model.