Related papers: Superefficiency from the Vantage Point of Computab…
This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…
Statistical convergence was introduced in connection with problems of series summation. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with…
We study the classical problem of deriving minimax rates for density estimation over convex density classes. Building on the pioneering work of Le Cam (1973), Birge (1983, 1986), Wong and Shen (1995), Yang and Barron (1999), we determine…
We study online changepoint detection in the context of a linear regression model. We propose a class of heavily weighted statistics based on the CUSUM process of the regression residuals, which are specifically designed to ensure timely…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
Measurements can be viewed as interactions between a measured system and a pointer system that imprint information about the system on the pointer. For so-called unbiased interactions, the measurement statistics--the information…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…
This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…
We consider a parametrised perturbation of a $\mathscr C^r$ diffeomorphism on a closed smooth Riemannian manifold with $r\geq 1$, modeled by nonautonomous dynamical systems. A point without time averages for a (nonautonomous) dynamical…
The smooth development of large parts of mathematics hinges on the idea that some sets are `small' or `negligible' and can therefore be ignored for a given purpose. The perhaps most famous smallness notion, namely `measure zero', originated…
We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a p-summability condition and for integration of functions from Lebesgue…
When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…
Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…
We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction…
Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous functions are well-behaved in that they are the pointwise…
We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a…
The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of…
This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give…
The stochastic efficiency [G. Verley et al., Nat. Commun. 5, 4721 (2014)] was introduced to evaluate the performance of energy-conversion machines in micro-scale. However, such an efficiency generally diverges when no heat is absorbed while…