Related papers: Nonlinear Sampling and Lebesgue's Integral Sums
As a generalization of the sum of digits function and other digital sequences, sequences defined as the sum of the output of a transducer are asymptotically analyzed. The input of the transducer is a random integer in $[0, N)$. Analogues in…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
We consider the problem of defining the significance of an itemset. We say that the itemset is significant if we are surprised by its frequency when compared to the frequencies of its sub-itemsets. In other words, we estimate the frequency…
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. We show that typically the natural dimension of these systems changes continuously with respect to the parameters that define the…
In 1973, E.J. McShane proposed an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used decide what tagged partitions are allowed. Such an approach does not require any preliminary knowledge of Measure…
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…
The Mixed Lebesgue space is a suitable tool for modelling and measuring signals living in time-space domains. And sampling in such spaces plays an important role for processing high-dimensional time-varying signals. In this paper, we first…
An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed.…
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…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…
Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…
Lienard systems of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with f(x) an even function, are studied in the strongly nonlinear regime ($\epsilon\to\infty$). A method for obtaining the number, amplitude and loci of the limit cycles of…
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns…
Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…