标题： 回归分位数过程的近似根号n 显示英文标题

标题： Nearly root-n approximation for regression quantile processes

摘要： 传统上，基于回归分位数的推断准确性评估依赖于巴哈杜尔表示法。 这在正态近似中提供了阶数为$n^{-1/4}$的误差，并表明基于回归分位数的推断可能不如基于其他（更平滑）方法的推断可靠，后者通常具有阶数为$n^{-1/2}$的误差（在某些特殊对称情况下甚至更好）。 幸运的是，广泛的模拟和经验应用表明，回归分位数的推断共享了其他程序的小误差率。 实际上，Komlós、Major 和 Tusnády 的“匈牙利”构造 [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131, Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] 为单样本分位数过程提供了一个替代展开，其误差率接近根号$n$（具体而言，偏差在一个因子$\log n$内）。 本文发展了这种展开，以提供一个理论基础，用于改进回归分位数模型中的推断近似。 一个独立有趣的应用结果是证明了对于条件推断，使用 Hall 和 Sheather [J. R. Stat. Soc. Ser. B Stat. Methodol. 50 (1988) 381-391] 的稀疏性估计方法时，覆盖概率的误差率与其单样本情况下的速率一致。 显示英文摘要

摘要： Traditionally, assessing the accuracy of inference based on regression quantiles has relied on the Bahadur representation. This provides an error of order $n^{-1/4}$ in normal approximations, and suggests that inference based on regression quantiles may not be as reliable as that based on other (smoother) approaches, whose errors are generally of order $n^{-1/2}$ (or better in special symmetric cases). Fortunately, extensive simulations and empirical applications show that inference for regression quantiles shares the smaller error rates of other procedures. In fact, the "Hungarian" construction of Koml\'{o}s, Major and Tusn\'{a}dy [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131, Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] provides an alternative expansion for the one-sample quantile process with nearly the root-$n$ error rate (specifically, to within a factor of $\log n$). Such an expansion is developed here to provide a theoretical foundation for more accurate approximations for inference in regression quantile models. One specific application of independent interest is a result establishing that for conditional inference, the error rate for coverage probabilities using the Hall and Sheather [J. R. Stat. Soc. Ser. B Stat. Methodol. 50 (1988) 381-391] method of sparsity estimation matches their one-sample rate.