On the wald,lagrangian multiplier and likelihood ratio tests when the information matrix is singular |
| |
Authors: | Abdalla T El-Helbawy Tawfik Hassan |
| |
Institution: | (1) Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt |
| |
Abstract: | Summary Modified formulas for the Wald and Lagrangian multiplier statistics are introduced and considered together with the likelihood
ratio statistics for testing a typical null hypothesisH
0 stated in terms of equality constraints. It is demonstrated, subject to known standard regularity conditions, that each of
these statistics and the known Wald statistic has the asymptotic chi-square distribution with degrees of freedom equal to
the number of equality constraints specified byH
0 whether the information matrix is singular or nonsingular. The results of this paper include a generalization of the results
of Sively (1959) concerning the equivalence of the Wald, Lagrange multiplier and likelihood ratio tests to the case of singular
information matrices. |
| |
Keywords: | Likelihood estimation subject to equality constraints Wald test Lagrangian multiplier test likelihood ratio test modified Wald and Lagrangian multiplier statistics equivalence of tests |
本文献已被 SpringerLink 等数据库收录! |