Comparison of the slope parameters in errors-in-variables model

Abstract

We consider the errors-in-variables model . We derive the likelihood ratio test for testing H ₀ : a ₁ = a ₂ under functional model, when U_i's are fixed and unknown. It is shown that the asymptotic distribution of the likelihood ratio test is a scalar multiple of a chi-square distribution. The similar result is obtained under structural model, when are distributed with some unknown arbitrary distribution. We also derive a small sample test statistics for testing H ₀ : a ₁ = a ₂ using a linearizing technique.

Keywords:

• Functional model
• structural model
• likelihood ratio test
• asymptotic distribution
• perturbation technique
• union-intersection principle