Related papers: Nonuniform average sampling in multiply generated …
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
In this paper we have considered the problem of estimating the population mean in systematic sampling using information on an auxiliary variable in presence of non response. Some modified ratio, product and difference type estimators in…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
Inequalities for product operators on mixed norm Lebesgue spaces and permuted mixed norm Lebesgue spaces are established. They depend only on inequalities for the factors and on the Lebesgue indices involved. Inequalities for the bivariate…
Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by…
A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be…
We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider…