A consistent specification test of independence

Abstract

This paper presents a new specification test of independence between two random vectors by the kernel method. The test statistic is shown to have asymptotic standard normal distribution under the null hypothesis of independence, while diverging to infinity if the null is false. Hence, the test is consistent against any form of dependence between the two random vectors. The power of the test against local alternatives is also investigated.

Keywords:

• Independence
• specification test
• consistent test
• kernel method
• local alternatives

AMS 1991 Subject Classification:

• Primary 62G10
• Secondary 62607