On testing linear hypotheses on linear functional and structural relationships

Abstract

We consider an errors in variables model are observed random vectors,μ i ’s are unobserved fixed or random vectorsA and b are unknown parameters, and ei ’sfi ’s are random error vectors. Bansal (1990) derived likelihood ratio tests, under functional relationship, for testing linear hypotheses: (i) H0 : AR = K and (ii) St A = L1 where R,K, S and L are known matrices. In this paper, we obtain the asymptotic distributions of the likelihood ratio test statistics under functional relationship. We also obtain the asymptotic distributions of these test statistics under structural relationship. Some special cases are considered and modified test statistics are given for these cases.