A1544
Title: Multivariate nonparametric Erlang mixtures
Authors: Kyeong-A Yang - Sungkyunkwan University (Korea, South) [presenting]
Byungtae Seo - Sungkyunkwan University (Korea, South)
Abstract: Multivariate positive-valued data arise in various applications, including insurance losses, survival outcomes, and waiting-time data, where skewness, heavy tails, and multimodality are commonly present. Multivariate Erlang mixtures provide a flexible and analytically tractable framework for modeling such data, with appealing properties including closure under marginalization and denseness in the class of positive continuous multivariate distributions. However, existing research has primarily focused on their structural properties and expectation-maximization (EM) based estimation under a fixed number of components. A nonparametric maximum likelihood estimator (NPMLE) for multivariate Erlang mixtures is considered, without pre-specifying the number of support points of the mixing distribution. The proposed approach uses a gradient function as a diagnostic tool to assess lack of fit and to identify promising support points. Numerical studies demonstrate that this method progressively refines the support and improves model fit for multivariate Erlang mixtures. These findings suggest that multivariate nonparametric Erlang mixtures serve as an effective and flexible framework for multivariate density estimation.
