Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests those which are consistent without any assumptions about how the distributions may differ (general alternatives), and t...

In this paper, we consider testing the equality of two mean vectors with unequal covariance matrices. In the case of equal covariance matrices, we can use Hotelling’s T 2 statistic, which follows the F distribution under the null hypothesis. Meanwhile, in the case of unequal covariance matrices, the T 2 type test statistic does not follow the F distribution, and it is also difficult to derive t...

In recent two decades, long-horizon regression has become a popular choice for testing mean reversion in stock prices. Due to overlapping and multi-period return summation, finite sample analysis of long-horizon regression coefficient is complicated and largely unavailable in the literature. Empirical studies almost entirely rely on asymptotic tests, which can have serious size distortions and ...

1. Introduction. The joint asymptotic distribution of the sample mean and the sample median was found by Laplace almost 200 years ago. See Stigler [2] for an interesting historical discussion of this achievement. For a review of other work on this problem, see derive the asymptotic joint distribution of the sample mean and an arbitrary quantile. It is hoped that the proof may be new and of inte...

This article obtains a general formula to find the correlation coefficient between the sample mean and variance. Several particular results for major non-normal distributions are extracted to help students in classroom, clients during statistical consulting service.