Maximum smoothed likelihood estimation for a class of semiparametric Pareto mixture densities

Motivated by an analysis of Return On Equity (ROE) data, we propose a class of semiparametric mixture models. The proposed models have a symmetric nonparametric component and a parametric component of Pareto distribution with unknown parameters. However, situations with general parametric components other than Pareto distribution are also investigated. We prove that these mixture models are identifiable, and establish a novel estimation procedure via smoothed likelihood and profile-likelihood techniques. For ease of computation, we develop a new EM algorithm to facilitate the maximization problem. We show that this EM algorithm possesses the ascent property. A rule-of-thumb based procedure is proposed to select the bandwidth of the nonparametric component. Simulation studies demonstrate good performance of the proposed methodology. Furthermore, we analyze the ROE dataset which may consist of real and manipulated earnings. Our analysis reveals significant earning manipulation in the Chinese listed companies from a quantitative perspective using the proposed model.