Convolution Mode Regression
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916513029554176 |
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| author | Finn, Eduardo Schirmer Horta, Eduardo |
| author_facet | Finn, Eduardo Schirmer Horta, Eduardo |
| contents | For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode regression) presents significant challenges. Nonparametric approaches suffer from the "curse of dimensionality", while semiparametric strategies often lead to non-convex optimization problems. In order to avoid these issues, we propose a novel mode regression estimator that relies on an intermediate step of inverting the conditional quantile density. In contrast to existing approaches, we employ a convolution-type smoothed variant of the quantile regression. Our estimator converges uniformly over the design points of the covariates and, unlike previous quantile-based mode regressions, is uniform with respect to the smoothing bandwidth. Additionally, the Convolution Mode Regression is dimension-free, carries no issues regarding optimization and preliminary simulations suggest the estimator is normally distributed in finite samples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convolution Mode Regression Finn, Eduardo Schirmer Horta, Eduardo Econometrics Statistics Theory For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode regression) presents significant challenges. Nonparametric approaches suffer from the "curse of dimensionality", while semiparametric strategies often lead to non-convex optimization problems. In order to avoid these issues, we propose a novel mode regression estimator that relies on an intermediate step of inverting the conditional quantile density. In contrast to existing approaches, we employ a convolution-type smoothed variant of the quantile regression. Our estimator converges uniformly over the design points of the covariates and, unlike previous quantile-based mode regressions, is uniform with respect to the smoothing bandwidth. Additionally, the Convolution Mode Regression is dimension-free, carries no issues regarding optimization and preliminary simulations suggest the estimator is normally distributed in finite samples. |
| title | Convolution Mode Regression |
| topic | Econometrics Statistics Theory |
| url | https://arxiv.org/abs/2412.05736 |