2023/11/25 by Ioannis Oikonomidis, Samis Trevezas, Oikonomidis, Ioannis +1
Computer Science · Decision Sciences · Mathematics · #Applied mathematics #Bayesian Methods and Mixture Models #Dirichlet distribution #Estimator #Mathematical analysis #Mathematics #Moment (physics) #Multivariate statistics #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistics #Type (biology)
paper · pdf · open access · doi:10.1016/j.jmva.2025.105471
published in Journal of Multivariate Analysis 210, 105471 (Elsevier BV)
openalex publication_date 2025/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators for the Beta and Gamma distributions, extending their applicability to the Dirichlet and Multivariate Gamma distributions. Expressions for the asymptotic variance-covariance matrices are provided, demonstrating the superior performance of score-adjusted estimators over the traditional moment ones. Leveraging well-established connections between Dirichlet and Multivariate Gamma distributions, a novel class of estimators for the latter is introduced, referred to as "Dirichlet-based moment-type estimators". The general asymptotic variance-covariance matrix form for this estimator class is derived. To facilitate the application of these innovative estimators, an R package called estimators is developed and made publicly available.