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1. Multiplier bootstrap for quantile regression: non-asymptotic theory under random design

   https://doi.org/10.1093/imaiai/iaaa006  

   Pan, Xiaoou; Zhou, Wen-Xin (May 2020, Information and Inference: A Journal of the IMA)

   null (Ed.)

   Abstract This paper establishes non-asymptotic concentration bound and Bahadur representation for the quantile regression estimator and its multiplier bootstrap counterpart in the random design setting. The non-asymptotic analysis keeps track of the impact of the parameter dimension $$d$$ and sample size $$n$$ in the rate of convergence, as well as in normal and bootstrap approximation errors. These results represent a useful complement to the asymptotic results under fixed design and provide theoretical guarantees for the validity of Rademacher multiplier bootstrap in the problems of confidence construction and goodness-of-fit testing. Numerical studies lend strong support to our theory and highlight the effectiveness of Rademacher bootstrap in terms of accuracy, reliability and computational efficiency. 

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2. Improving comparison of power and level for conservative multiplier bootstrap tests in simulation studies and beyond

   https://doi.org/10.5281/zenodo.17019775  

   Sakhanenko, Lyudmila (January 2025, Zenodo)

   We propose a simple modification procedure that helps to compare the levels and powers for conservative multiplier bootstrap tests. It is especially useful for simulation studies where empirical levels are zero. We provide a theoretical justification and illustrate the use of the procedure in a recent class of multiplier bootstrap tests for quantile regression and in a recent class of high-dimensional tests for MANOVA. 

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3. Semiparametric estimation of structural functions in nonseparable triangular models

   https://doi.org/10.3982/QE1239  

   Chernozhukov, Victor; Fernández-Val, Iván; Newey, Whitney; Stouli, Sami; Vella, Francis (January 2020, Quantitative Economics)

   Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modeling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these limitations. They are based on distribution and quantile regression modeling of the reduced form conditional distributions of the endogenous variables. We show that average, distribution, and quantile structural functions are identified in these systems through a control function approach that does not require a large support condition. We propose a computationally attractive three‐stage procedure to estimate the structural functions where the first two stages consist of quantile or distribution regressions. We provide asymptotic theory and uniform inference methods for each stage. In particular, we derive functional central limit theorems and bootstrap functional central limit theorems for the distribution regression estimators of the structural functions. These results establish the validity of the bootstrap for three‐stage estimators of structural functions, and lead to simple inference algorithms. We illustrate the implementation and applicability of all our methods with numerical simulations and an empirical application to demand analysis. 

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4. Subsampling to Enhance Efficiency in Input Uncertainty Quantification

   https://doi.org/10.1287/opre.2021.2168  

   Lam, Henry; Qian, Huajie (January 2021, Operations Research)

   In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the nonparametric setting, is commonly estimated via the bootstrap. However, due to the convolution of the simulation noise and the input noise, the bootstrap consists of a two-layer sampling and typically requires substantial simulation effort. This paper investigates a subsampling framework to reduce the required effort, by leveraging the form of the variance and its estimation error in terms of the data size and the sampling requirement in each layer. We show how the total required effort can be reduced from an order bigger than the data size in the conventional approach to an order independent of the data size in subsampling. We explicitly identify the procedural specifications in our framework that guarantee relative consistency in the estimation and the corresponding optimal simulation budget allocations. We substantiate our theoretical results with numerical examples. 

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5. Highly parallelized data-driven MPC for minimal intervention shared control

   https://doi.org/10.15607/RSS.2019.XV.008  

   Broad, A.; Murphey, T.; Argall, B. (June 2019, Robotics: science and systems)

   We present a shared control paradigm that improves a user’s ability to operate complex, dynamic systems in potentially dangerous environments without a priori knowledge of the user’s objective. In this paradigm, the role of the autonomous partner is to improve the general safety of the system without constraining the user’s ability to achieve unspecified behaviors. Our approach relies on a data-driven,model-based representation of the joint human-machine system to evaluate, in parallel, a significant number of potential inputs that the user may wish to provide. These samples are used to (1)predict the safety of the system over a receding horizon, and (2)minimize the influence of the autonomous partner. The resulting shared control algorithm maximizes the authority allocated to the human partner to improve their sense of agency, while improving safety. We evaluate the efficacy of our shared control algorithm with a human subjects study (n=20) conducted in two simulated environments: a balance bot and a race car. During the experiment, users are free to operate each system however they would like (i.e., there is no specified task) and are only asked to try to avoid unsafe regions of the state space. Using modern computational resources (i.e., GPUs) our approach is able to consider more than 10,000 potential trajectories at each time step in a control loop running at 100Hz for the balance bot and 60Hzfor the race car. The results of the study show that our shared control paradigm improves system safety without knowledge of the user’s goal, while maintaining high-levels of user satisfaction and low-levels of frustration. Our code is available online athttps://github.com/asbroad/mpmisharedcontrol. 

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