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Convolution Mode Regression

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  • Eduardo Schirmer Finn
  • Eduardo Horta

Abstract

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.

Suggested Citation

  • Eduardo Schirmer Finn & Eduardo Horta, 2024. "Convolution Mode Regression," Papers 2412.05736, arXiv.org.
    • Handle: RePEc:arx:papers:2412.05736
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    References listed on IDEAS

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