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We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based…

Uncertainty quantification, by means of confidence interval (CI) construction, has been a fundamental problem in statistics and also important in risk-aware decision-making. In this paper, we revisit the basic problem of CI construction,…

I propose a nonparametric iid bootstrap procedure for the empirical likelihood, the exponential tilting, and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals,…

We consider the problem of adaptively placing sensors along an interval to detect stochastically-generated events. We present a new formulation of the problem as a continuum-armed bandit problem with feedback in the form of partial…

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction…

For an autonomous agent, executing a poor policy may be costly or even dangerous. For such agents, it is desirable to determine confidence interval lower bounds on the performance of any given policy without executing said policy. Current…

Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a…

We consider the problem of constructing differentially private nonparametric confidence intervals (CIs) for an arbitrary quantity using resampling. A growing body of work has adapted resampling ideas to the private setting, including…

We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and…

Learning-based methodologies increasingly find applications in safety-critical domains like autonomous driving and medical robotics. Due to the rare nature of dangerous events, real-world testing is prohibitively expensive and unscalable.…

Bayesian inference is a principled framework for dealing with uncertainty. The practitioner can perform an initial assumption for the physical phenomenon they want to model (prior belief), collect some data and then adjust the initial…

This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…

The bootstrap variance estimate is widely used in semiparametric inferences. However, its theoretical validity is a well known open problem. In this paper, we provide a {\em first} theoretical study on the bootstrap moment estimates in…

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap.…

Effective collective decision-making in swarm robotics often requires balancing exploration, communication and individual uncertainty estimation, especially in hazardous environments where direct measurements are limited or costly. We…

Accurate EV power estimation underpins range prediction and energy management, yet practitioners need both point accuracy and trustworthy uncertainty. We propose an anchored-ensemble Long Short-Term Memory (LSTM) with a Student-t likelihood…

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual…

Several factors affect the structure of communities, including biological, physical and chemical phenomena, impacting the quantification of biodiversity, measured by diversity indexes such as Shannon's entropy. Then, once a point estimate…