Scalable estimation and inference for censored quantile regression process
Scalable estimation and inference for censored quantile regression process
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DOI：
10.1214/22-aos2214
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发表时间：
2022-10
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通讯作者：
Xuming He;Xiaoou Pan;Kean Ming Tan;Wen-Xin Zhou
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作者：
Xuming He;Xiaoou Pan;Kean Ming Tan;Wen-Xin Zhou
删失分位数回归（CQR）已成为研究可能删失结果和协变量之间异质关联的重要工具，但对于包含多个协变量的大规模数据，CQR的计算和统计推断仍然是一个挑战。在本文中，我们专注于一个平滑的鞅为基础的序列估计方程的方法，可扩展的基于梯度的算法可以应用。在理论上，我们提供了一个统一的分析光滑序列估计和它的惩罚对应的增加的维度。当协变量维数增长的样本量在一个次线性率，我们建立了统一的收敛速度（在一个范围内的分位数指数），并提供了一个严格的理由的有效性的乘数引导过程的推断。在高维稀疏设置，我们的研究结果大大提高了现有的工作CQR放松指数项的稀疏性。我们还展示了平滑CQR的优势，现有的方法与模拟实验和数据应用。
Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge for large-scale data with many covariates. In this paper, we focus on a smoothed martingale-based sequential estimating equations approach, to which scalable gradient-based algorithms can be applied. Theoretically, we provide a unified analysis of the smoothed sequential estimator and its penalized counterpart in increasing dimensions. When the covariate dimension grows with the sample size at a sublinear rate, we establish the uniform convergence rate (over a range of quantile indexes) and provide a rigorous justification for the validity of a multiplier bootstrap procedure for inference. In high-dimensional sparse settings, our results considerably improve the existing work on CQR by relaxing an exponential term of sparsity. We also demonstrate the advantage of the smoothed CQR over existing methods with both simulated experiments and data applications.