{"ID":2846453,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.01153","arxiv_id":"2511.01153","title":"Consistent estimation in subcritical birth-and-death processes","abstract":"We investigate parameter estimation in subcritical continuous-time birth-and-death processes with multiple births. We show that the classical maximum likelihood estimators for the model parameters, based on the continuous observation of a single non-extinct trajectory, are not consistent in the usual sense: conditional on survival up to time $t$, they converge as $t \\to \\infty$ to the corresponding quantities in the associated $Q$-process, namely the process conditioned to survive in the distant future. We develop the first $C$-consistent estimators in this setting, which converge to the true parameter values when conditioning on survival up to time $t$, and establish their asymptotic normality. The analysis relies on spine decompositions and coupling techniques.","short_abstract":"We investigate parameter estimation in subcritical continuous-time birth-and-death processes with multiple births. We show that the classical maximum likelihood estimators for the model parameters, based on the continuous observation of a single non-extinct trajectory, are not consistent in the usual sense: conditional...","url_abs":"https://arxiv.org/abs/2511.01153","url_pdf":"https://arxiv.org/pdf/2511.01153v1","authors":"[\"Sophie Hautphenne\",\"Emma Horton\"]","published":"2025-11-03T02:04:23Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}