Empirical likelihood ratio test with density function constraints

Abstract

In this work, we study non-parametric hypothesis testing problem with density function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some detection problems cannot be described using moment (in)equalities. We propose a density function constraint along with an empirical likelihood ratio test. This detector is applicable to a wide variety of robust parametric/non-parametric detection problems. Since the density function constraints provide a more exact description of the null hypothesis, the test outperforms many other alternatives such as the empirical likelihood ratio test with moment constraints and robust Kolmogorov-Smirnov test, especially when the alternative hypothesis has a special structure.