Student's t-test without symmetry conditions

TL;DR

This paper introduces a new method for testing asymmetry and location in distributions without requiring symmetry, using a mixture representation of zero-mean distributions to develop exact inequalities and tests.

Contribution

It provides an explicit mixture representation for any zero-mean distribution and constructs new tests for asymmetry and location that do not depend on symmetry assumptions.

Findings

Derived explicit mixture representation for zero-mean distributions

Developed tests for asymmetry and location without symmetry conditions

Established exact inequalities ensuring test conservativeness

Abstract

An explicit representation of an arbitrary zero-mean distribution as the mixture of (at-most-)two-point zero-mean distributions is given. Based in this representation, tests for (i) asymmetry patterns and (ii) for location without symmetry conditions can be constructed. Exact inequalities implying conservative properties of such tests are presented. These developments extend results established earlier by Efron, Eaton, and Pinelis under a symmetry condition.