A conditional composite likelihood ratio test with boundary constraints
Yong Chen, Jing Yang Huang, Yang Ning, Kung‐Yee Liang, Bruce G. Lindsay · Biometrika · 2017
Composite likelihood has been widely used in applications. The asymptotic distribution of the composite likelihood ratio statistic at the boundary of the parameter space is a complicated mixture of weighted |$\chi^2$| distributions. In this paper we propose a conditional test with data-dependent degrees of freedom. We consider a modification of the composite likelihood which satisfies the second-order Bartlett identity. We show that the modified composite likelihood ratio statistic given the number of estimated parameters lying on the boundary converges to a simple |$\chi^2$| distribution. This conditional testing procedure is validated through simulation studies.