In this article, the empirical likelihood introduced by Owen Biometrika, 75, 237-249 （1988） is applied to test the variances of two populations under inequality constraints on the parameter space. One reason that we do the research is because many literatures in this area are limited to testing the mean of one population or means of more than one populations; the other but much more important reason is： even if two or more populations are considered, the parameter space is always without constraint. In reality, parameter space with some kind of constraints can be met everywhere. Nuisance parameter is unavoidable in this case and makes the estimators unstable. Therefore the analysis on it becomes rather complicated. We focus our work on the relatively complicated testing issue over two variances under inequality constraints, leaving the issue over two means to be its simple ratiocination. We prove that the limiting distribution of the empirical likelihood ratio test statistic is either a single chi-square distribution or the mixture of two equally weighted chi-square distributions.
This study is to use cointegration, linear and non-linear Granger causality test to investigate the relationship between carbon dioxide （CO2） emissionand economic growth （GDP） in China for the period 1961-2010. Our analysis shows that CO2 emission and GDP are balanced in the long-run. The results suggest that there is evidence that economic development can improve environmental degradation in the long-run. Moreover, the result of linear and non-linear Granger causality test indicates a long-run unidirectional causality running from GDP to CO2 emissions. The study suggests that in the long run, economic growth may have an adverse effect on the CO2 emissions in China. Government should take into account the environment in their current policies, which may be of great importance for policy decision-makers to develop economic policies to preserve economic growth while curbing of carbon emissions.
