Some novel applications of empirical likelihood methods
MetadataShow full item record
We present some novel applications of empirical likelihood approach on a few topics. First, under the framework of the empirical likelihood method, hypothesis testing with general U-statistics type of constraints is investigated. Tests for the area under the receiver operating characteristic curve (AUC) or correlated AUC’s can be fitted into such situations. We show that the resulting empirical likelihood ratio statistic has a weighted χ 2 distribution (univariate cases) or a combination of weighted χ 2 distributions (multivariate cases). Second, we investigate the partial AUC (pAUC). The pAUC is commonly estimated based on a U-statistic. However, common variance estimation strategies for U-statistics severely overestimate the variance of the pAUC estimator. We propose a method to obtain the variance of the nonparametric pAUC estimator accurately and develop an empirical likelihood inference method based on the proposed variance estimator. Finally, using the EL approach incorporating the kernel density estimation, we propose the nonparametric test statistic of two sample modes comparison that can be applied for different underlying distributions. We compare the proposed method with the bootstrap method. Further, we apply the proposed method to investigate a change of income modes over years for interested populations using American Community Survey data.