A monotonic MM-type algorithm for estimation of nonparametric finite mixture models with dependent marginals
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912387839295488 |
|---|---|
| author | Levine, Michael |
| author_facet | Levine, Michael |
| contents | In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms capable of estimating components of such a model have been available. A deterministic algorithm that is capable of this has been proposed in \citet*{levine2024smoothed}. That algorithm seeks to maximize a smoothed nonparametric penalized log-likelihood; it seems to perform well in practice but does not possess the monotonicity property. In this manuscript, we introduce a deterministic MM (Minorization-Maximization) algorithm for estimation of components of this model that is also maximizing a smoothed penalized nonparametric log-likelihood but that is monotonic with respect to this objective functional. Besides the convergence of the objective functional, the convergence of a subsequence of arguments of this functional, generated by this algorithm, is also established. The behavior of this algorithm is illustrated using both simulated datasets as well as a real dataset. The results illustrate performance that is at least comparable to the earlier algorithm of \citet*{levine2024smoothed}. A discussion of the results and possible future research directions make up the last part of the manuscript. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A monotonic MM-type algorithm for estimation of nonparametric finite mixture models with dependent marginals Levine, Michael Methodology Computation 62G07, 62H30 In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms capable of estimating components of such a model have been available. A deterministic algorithm that is capable of this has been proposed in \citet*{levine2024smoothed}. That algorithm seeks to maximize a smoothed nonparametric penalized log-likelihood; it seems to perform well in practice but does not possess the monotonicity property. In this manuscript, we introduce a deterministic MM (Minorization-Maximization) algorithm for estimation of components of this model that is also maximizing a smoothed penalized nonparametric log-likelihood but that is monotonic with respect to this objective functional. Besides the convergence of the objective functional, the convergence of a subsequence of arguments of this functional, generated by this algorithm, is also established. The behavior of this algorithm is illustrated using both simulated datasets as well as a real dataset. The results illustrate performance that is at least comparable to the earlier algorithm of \citet*{levine2024smoothed}. A discussion of the results and possible future research directions make up the last part of the manuscript. |
| title | A monotonic MM-type algorithm for estimation of nonparametric finite mixture models with dependent marginals |
| topic | Methodology Computation 62G07, 62H30 |
| url | https://arxiv.org/abs/2505.16878 |