An Efficient Convex-Inclusion Classifier Through Depth Notion Based on Empirical Likelihood Function
摘要
The empirical likelihood is a fully data-dependent nonparametric inference framework. It requires comparatively fewer distributional assumptions but retains many desirable properties of the parametric likelihood approach. Motivated by the empirical likelihood and depth functions based on empirical likelihood, we propose a new classifier based on generalized empirical depth (GED) in this paper. Existing classifiers based on the halfspace and the zonoid depth suffer from the outsider problem, where observations outside the convex hull receive zero depth values. To fill this gap, the proposed method provides a convex-inclusion mechanism that assigns meaningful depth values to all observations and eliminates the outsider problem. A pseudo-population version of the procedure is also established and asymptotic consistency behavior of the procedure is discussed under mild conditions. Unlike existing empirical likelihood-based methods, the proposed method has an advantage of having non-degenerate population analogue. The performance of the proposed approach is examined using simulated as well as real datasets, and the results are compared with those based on the zonoid and empirical depths. Comparisons with the other classifiers show that the proposed method performs competitively across a wide range of settings. It achieves noticeable improvements in scenarios where the outsider problem exists.