Mixture Quantiles Estimated by Constrained Linear Regression
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914304532414464 |
|---|---|
| author | Peng, Cheng Li, Yizhou Uryasev, Stan |
| author_facet | Peng, Cheng Li, Yizhou Uryasev, Stan |
| contents | We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its parameters, estimation reduces to constrained linear regression, yielding a convex optimization problem that readily accommodates cardinality constraints as well as L1 or smoothness regularization. For Lq-type objectives we show the estimator is asymptotically equivalent to a minimum q-Wasserstein distance estimator and establish asymptotic normality. Experiments on simulated and real-world datasets demonstrate that the proposed method accurately captures both the central body and extreme tails of distributions while requiring substantially less computation than standard benchmark approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00081 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mixture Quantiles Estimated by Constrained Linear Regression Peng, Cheng Li, Yizhou Uryasev, Stan Methodology We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its parameters, estimation reduces to constrained linear regression, yielding a convex optimization problem that readily accommodates cardinality constraints as well as L1 or smoothness regularization. For Lq-type objectives we show the estimator is asymptotically equivalent to a minimum q-Wasserstein distance estimator and establish asymptotic normality. Experiments on simulated and real-world datasets demonstrate that the proposed method accurately captures both the central body and extreme tails of distributions while requiring substantially less computation than standard benchmark approaches. |
| title | Mixture Quantiles Estimated by Constrained Linear Regression |
| topic | Methodology |
| url | https://arxiv.org/abs/2305.00081 |