On a multivariate normal linear regression hypothesis testing problem with additional observations

Abstract

Given the first multivariate normal linear regression model with (p+q)×n Y and p×n Y₁, and the second additional multivariate normal linear regression model Y₀=B₁Z+E₁, with Y₀ pxm, m ≥ n, Sarkar (1981) poses the following hypothesis testing problem. Test B₂v=0 against B₂ ≠ 0 given B₁=0 and a specified V. He provides an ad hoc nuisance parameter removal test for this problem. A slightly different ad hoc nuisance parameter removal test for this problem, whose derivation is based on generalized Sverdrup's lemma, Kabe (1965), is presented in this paper.

Keywords:

• Hypothesis testing
• GMANOVA model
• SUR model nuisance parameter removal test