Empirical likelihood ratio test for or against a set of inequality constraints

Empirical likelihood hypothesis test on mean with inequality constraints

“…It is worth noting that the result in our Theorem 2.1 can be derived by El Barmi [1], but our proofs are new and different from that of El Barmi [1].…”

“…El Barmi's method [1] relies heavily on the theory of Qin and Lawless [8]. Therefore, using the same assumption as in Qin and Lawless [8], El Barmi [1] requires that the number of inequality constraint g(θ) 0 must be less than or equal to the dimension number of θ.…”

“…It can be called the irregular case. For the mean case, El Barmi's result [1] can be applied to one-sided hypothesis test. However, it fails to test the two-sided and composite hypotheses.…”

“…The classical normal approximation approach does not seem to be readily applicable because the interval information is hard to be incorporated into estimation of the mean. El Barmi [1] studied the empirical likelihood ratio hypothesis tests when the parameter of interest satisfies a set of inequalities. Based on the results of Qin and Lawless [8], El Barmi [1] showed that limiting distribution of the empirical log-likelihood ratio statistics is chi-bar square, i.e., a weighted mixture of chi-square distributions.…”

“…However, Moon and Schorfheide's model [2] does not seem to be applicable to the mean problem. Limitation of El Barmi [1] and Moon and Schorfheide [2] will be addressed in the discussion section.…”