Martingale posteriors quantify uncertainty by forward-imputing observations from one-step-ahead predictive distributions, but implementations stop after finitely many imputations. For the empirical P\'olya-urn posterior of a quantile the law of the stopped state is derived. The quantile of the stopped urn measure keeps the familiar martingale tail-sum variance fraction; the deployed stochastic-approximation tracker with frozen gain $c$ does not. Its variance carries an explicit factor $G_a$ with $a=cf_0(q_\tau)$, which may fall below or exceed the tail fraction, and a density-adapted gain restores calibration through a density-free inflation. Shared urn innovations yield the joint law of finitely many quantile levels. For conditional quantile regression, a smoothed martingale posterior started at the ordinary quantile-regression estimator with a full inverse-Jacobian matrix gain satisfies a process Bernstein--von Mises theorem with calibrated finite-horizon bands; scalar or diagonal gains cannot match the sandwich covariance process.
A global high-probability last-iterate guarantee for synchronous tabular QTD under general positive, nonincreasing step-size sequences and arbitrary initialization in the natural parameter range is established.
Zijie Cheng, Xiang Li, Yang Peng et al.· 0 citations
Results demonstrate that adaptive finite-budget training design, applied solely to the training procedure without altering the risk objective, can materially improve the reliability and risk-adjusted performance of risk-aware Q-learning in financial applications.
This work proposes deep nonparametric Instrumental variable quantile regression (IVQR), a two-stage estimator that combines conditional diffusion modeling with a kernel-smoothed conditional moment formulation and derives end-to-end total variation guarantees for the conditional diffusion model under unbounded support.
Xingdong Feng, Xinhong Jiang, Yu-Ling Jiao et al.· 0 citations
A distributed stochastic smoothing alternating direction method of multipliers (DSS-ADMM) for horizontally partitioned penalized quantile regression, which characterize the scope of an extension to the minimax concave penalty and the smoothly clipped absolute deviation penalty.
This work introduces a Markov chain Monte Carlo (MCMC) kernel that mixes better than existing samplers at the same computational complexity, and introduces a Sequential Monte Carlo squared sampler, which delivers at every $t$ the one-step-ahead predictive density and the marginal likelihood of the data up to $t, and he...
N. Chopin, Andras Fulop, Yu-Ming Huo et al.· 0 citations
A local asymptotic theory is developed for the estimated return CDF over $T^{-1/2}$-neighborhoods of finitely many thresholds, together with its bootstrap analogue that justifies bootstrap inference for smooth statistical functionals, including variance, CVaR, expected shortfall, and expectiles.
Peng Yang, Liangyu Zhang· 1 citation
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