Related papers: Consistent estimation of non-bandlimited spectral …
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…
This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into…
We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…
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)…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series,…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and proposes solutions to a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations?…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
In frequency domain analysis for spatial data, spectral averages based on the periodogram often play an important role in understanding spatial covariance structure, but also have complicated sampling distributions due to complex variances…
This paper discusses sample allocation problem (SAP) in frequency-domain Compressive Sampling (CS) of time-domain signals. An analysis that is relied on two fundamental CS principles; the Uniform Random Sampling (URS) and the Uncertainty…
A boson sampling device is a specialised quantum computer that solves a problem which is strongly believed to be computationally hard for classical computers. Recently a number of small-scale implementations have been reported, all based on…
The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…