arXiv subjects

Yunhao Yan

Publications and source records attributed to Yunhao Yan.

2 recordsLinked to original sources

arXiv2026

Studentized Cheap Bootstrap: Achieving Higher-Order Coverage Accuracy with Low Computation

The bootstrap is a versatile method for quantifying statistical uncertainty. Among its variants, a popular approach, the studentized bootstrap, provably achieves higher-order coverage error reduction compared to other benchmarks. However, its implementation typically requires an analytical form of the standard error, or otherwise an additional layer of resampling effort which can be computationally expensive. In this paper, we introduce what we call the studentized cheap bootstrap that achieves the same higher-order coverage accuracy as the conventional studentization, but substantially thinning the computational effort in the additional resampling layer to only very few Monte Carlo replications. Intriguingly, while conventional wisdom views "studentization" as an informal link between the bootstrap and t-distribution, we provide a first recognition that this link is in fact formal, notably with a distinct insight that the degree of freedom in the t-distribution corresponds to the Monte Carlo computation effort in the additional resampling layer, rather than the data size as in traditional thinking. Moreover, our desirable higher-order coverage accuracy builds crucially on this insight, as well as explicit calculations and geometric analyses of higher-order terms in the Edgeworth and Cornish-Fisher expansions tailored to limiting t-distributions.

stat.ME↗

arXiv2026

QPLEX Decision Processes: Formulation via Nonlinear Markov Chains and Optimization via Policy Gradients

We introduce a QPLEX Decision Process (QDP) as a model for dynamic control of queueing systems with non-stationary arrivals, general service distributions, and service-level chance constraints. QDPs integrate QPLEX, a computational modeling methodology for transient analysis of stochastic systems, into a nonlinear Markov decision framework. Since QPLEX approximations use nonlinear transition probabilities with orders-of-magnitude smaller state spaces, QDPs circumvent the curse of dimensionality associated with general service times. Via forward and backward iterative schemes, we can rapidly compute gradients deterministically on the much smaller state space, eliminating sampling variance. We further address optimization through natural-gradient-inspired methods with block-diagonal Fisher approximations. To illustrate the QDP methodology, we formulate a single-station dynamic pricing problem with non-stationary demand as a QDP. When the reward structure uses waiting and terminal costs, our approach can find near-optimal policies in seconds on a single CPU; when the reward structure uses penalties for deviating from service-level chance constraints, the optimization landscape is substantially more challenging yet our approach can find a high-quality, practical policy in approximately a minute on a single CPU.

math.OC↗