Related papers: Analyticity and supershift with irregular sampling
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
Randomized clinical trials are the gold standard when estimating the average treatment effect. However, they are usually not a random sample from the real-world population because of the inclusion/exclusion rules. Meanwhile, observational…
The main result states that every convex set-valued function defined on a real interval with compact values in a locally convex space, admits an affine selection. In the case if the target space is a real line and the values are closed real…
The sampling of functions of bounded variation (BV) is a long-standing problem in op- timization. The ability to sample such functions has relevance in the field of variational inverse problems, where the standard theory fails to guarantee…
The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
We are concerned with the problem of real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata…
Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
There is widespread confusion about the role of projectivity in likelihood-based inference for random graph models. The confusion is rooted in claims that projectivity, a form of marginalizability, may be necessary for likelihood-based…
There has long been an impression that reliabilism implies externalism and that frequentist statistics, due to its reliabilist nature, is inherently externalist. I argue, however, that frequentist statistics can plausibly be understood as a…
The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…