{"ID":2845268,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04226","arxiv_id":"2511.04226","title":"Rates of Convergence of Maximum Smoothed Log-Likelihood Estimators for Semi-Parametric Multivariate Mixtures","abstract":"Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus is on the estimator that maximizes a smoothed log-likelihood function, which can be efficiently computed using a majorization-minimization algorithm. This smoothed likelihood applies a nonlinear regularization operator defined as the exponential of a kernel convolution on the logarithm of each component density. Consistency of the estimators is demonstrated by leveraging classical M-estimation frameworks under mild regularity conditions. Subsequently, convergence rates for both finite- and infinite-dimensional parameters are derived by exploiting structural properties of the smoothed likelihood, the behavior of the iterative optimization algorithm, and a thorough study of the profile smoothed likelihood. This work provides the first rigorous theoretical guarantees for this estimation approach, bridging the gap between practical algorithms and statistical theory in semi-parametric mixture modeling.","short_abstract":"Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus is on the estimator that maximizes a smoothed log-likelihood function, which can...","url_abs":"https://arxiv.org/abs/2511.04226","url_pdf":"https://arxiv.org/pdf/2511.04226v1","authors":"[\"Marie Du Roy de Chaumaray\",\"Michael Levine\",\"Matthieu Marbac\"]","published":"2025-11-06T09:54:31Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}