We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating the application of distributed selective inference. For valid post-selection inference, a randomized procedure is introduced, in which the Lasso selection event is characterized through the associated Karush-Kuhn-Tucker conditions and the conditional distribution of the aggregated estimator is derived given the selection event. The resulting algorithm requires only three rounds of communication between local machines and the central server. Under standard regularity conditions, we establish the asymptotic validity of the proposed procedure and develop a large-deviation approximation to the selective likelihood for computationally tractable implementation. Simulation studies and a real-data application demonstrate the satisfactory finite-sample performance of the proposed method.
We propose a framework for estimating conditional extreme quantile treatment effects (CEQTEs) in observational studies with heavy-tailed outcomes. Our procedure first estimates intermediate conditional quantiles using inverse-probability-weighted (IPW) quantile regression and then extrapolates them to extreme levels us...
Xiao-Rui Wang, Juan Cai, H. J. Wang et al.· 0 citations
This paper studies online quantile regression for large-scale and streaming data using Stochastic SubGradient Descent (SSGD) with constant learning rates. Classical offline inference for quantile regression is computationally and memory intensive. Existing works of online inference for quantile regression provide only...
Zi-Yang Wei, Jia-Qi Li, Lan Wang et al.· 0 citations
This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uni...
Kai-Cheng Chen, Antonio F. Galvao, Seunghwa Rho et al.· 0 citations
Reinforcement learning and contextual bandit algorithms have become increasingly common in sequential decision-making applications. When these methods are deployed in high-stakes domains, there is growing interest not only in learning effective policies, but also in conducting statistical inference for quantities learn...
James Leiner, Aurélien F. Bibaut, Nathan Kallus et al.· 0 citations
Sequential quantile inference is difficult under local differential privacy because every record is randomized before reaching the analyst and the limiting quantile variance depends on an unknown density. We develop an online procedure that combines randomized response with dynamically chained parallel stochastic gradi...
Estimating extreme conditional quantiles faces two major challenges: understanding complex nonlinear relationships between variables and accurately extrapolating into the tails of the distribution, where data are sparse. To address both issues, we introduce a novel approach that combines the theoretical framework of bl...
Lucien M. Vidagbandji, Alexandre Berred, Cyrille Bertelle et al.· 0 citations
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