THE RATE FUNCTION OF S-MIXING PROCESS AND ITS APPLICATION IN EVALUATING EMPIRICAL LIKELIHOOD TESTS

In this study we show that the rate function of S-Mixing stationary process with part of the hypermixing condition is equivalent to the Kullback-Leibler distance. This finding can be used to extend the result of the optimality of empirical likelihood test in i.i.d setting to weakly depended case, so that the Asymptotic Relative Efficiency (ARE) of the empirical likelihood test with strong mixing data can be established.