| 讲座简介： | Standard quantile regression suffers from high variability in the tail regions, particularly for heavy-tailed data. As the quantile level approaches 1 or 0, the estimator exhibits non-standard asymptotic behavior, posing challenges for statistical inference. In this paper, we propose a novel tail-reinforced quantile regression estimator that substantially reduces estimation variance by leveraging the power-law behavior inherent in heavy-tailed distributions. Our estimator is both consistent and asymptotically normal. To facilitate inference, we further introduce a sequential multiplier bootstrap procedure using multiple sets of random weights. Simulation studies demonstrate that our method yields notably narrower confidence intervals compared to standard quantile regression, while achieving near-exact coverage through the bootstrap procedure. We apply the proposed method to assess the marginal effect of education on upper income percentiles using a unique dataset from the Chinese Twins Survey. The results reveal a significantly positive effect of education in the upper tail, in contrast to existing approaches, which often yield insignificant effects accompanied by wide confidence intervals. |
