A general semi-parametric elliptical distribution model for semi-supervised learning

This research proposes a novel semi-parametric elliptical distribution model for application in semi-supervised learning tasks. We use labelled and unlabelled data to develop a pseudo maximum likelihood method for estimation and classification. The proposed estimator outperforms the estimator based solely on labelled data and achieves the semi-parametric efficiency bound with a suitable size of unlabelled data. We efficiently maximise the objective function by utilising low-dimensional groupwise pseudo-likelihood functions in a block coordinate descent manner while ensuring numerical stability and convergence through appropriate bandwidth selectors and initial parameter estimates. Additionally, the study comprehensively investigates the impact of labelled and unlabelled data on the pseudo maximum likelihood estimator and classifier. Simulation studies and empirical data applications illustrate the superiority of our methodology.