标题： 卷积模式回归 显示英文标题

标题： Convolution Mode Regression

摘要： 对于高度偏斜或肥尾分布，基于均值或中位数的方法通常无法捕捉数据中的中心趋势。尽管条件模式（或模式回归）估计给定某些协变量的条件模式是一种可行的替代方法，但它也面临着重大挑战。非参数方法受到“维度诅咒”的影响，而半参数策略往往会导致非凸优化问题。为了避开这些问题，我们提出了一种新的模式回归估计器，该估计器依赖于条件分位数密度的逆转换的中间步骤。与现有方法不同的是，我们采用了分位数回归的卷积型平滑变体。我们的估计器在协变量的设计点上一致收敛，并且与之前的基于分位数的模式回归不同，它相对于平滑带宽是一致的。此外，卷积模式回归不受维度限制，没有优化问题，并且初步模拟表明该估计器在有限样本中呈正态分布。 显示英文摘要

摘要： 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.