Related papers: Asymptotic Validity and Finite-Sample Properties o…
Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with…
For multi-class classification under class-conditional label noise, we prove that the accuracy metric itself can be robust. We concretize this finding's inspiration in two essential aspects: training and validation, with which we address…
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference…
This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Such asymptotic regime occurs when the system starts from…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
Asymptotic theory for M-estimation problems usually focuses on the asymptotic convergence of the sample descriptor, defined as the minimizer of the sample loss function. Here, we explore a related question and formulate asymptotic theory…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include…
We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial input uncertainty, but researchers…
We investigate the asymptotic behavior, in the long time limit, of the random homology associated to realizations of stochastic diffusion processes on a compact Riemannian manifold. In particular a rigidity result is established: if the…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
Randomized smoothing has achieved great success for certified robustness against adversarial perturbations. Given any arbitrary classifier, randomized smoothing can guarantee the classifier's prediction over the perturbed input with…
In this paper we study the effects of noise on the bipower variation (BPV), realized volatility (RV) and testing for co-jumps in high-frequency data under the small noise framework. We first establish asymptotic properties of the BPV in…