Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.04226 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- 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.