Related papers: Least absolute deviation estimation for AR(1) proc…
Given a directed graph, the Minimum Feedback Arc Set (FAS) problem asks for a minimum (size) set of arcs in a directed graph, which, when removed, results in an acyclic graph. In a seminal paper, Berger and Shor [1], in 1990, developed…
The Laguerre functions $l_{n,\tau}^\alpha$, $n=0,1,\dots$, are constructed from generalized Laguerre polynomials. The functions $l_{n,\tau}^\alpha$ depend on two parameters: scale $\tau>0$ and order of generalization $\alpha>-1$, and form…
We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence…
We establish the fundamental limits of lossless analog compression by considering the recovery of arbitrary m-dimensional real random vectors x from the noiseless linear measurements y=Ax with n x m measurement matrix A. Our theory is…
A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if $f$ is a Besicovitch almost periodic function and $V$ is a random variable uniformly…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
Low Diameter Decompositions (LDDs) are invaluable tools in the design of combinatorial graph algorithms. While historically they have been applied mainly to undirected graphs, in the recent breakthrough for the negative-length Single Source…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…
In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily…
When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…
We develop an asymptotic statistical theory for parameter estimation from a class of non-i.i.d. periodic binary event-detection processes subject to nonparalyzable dead time and gating, which we call "dead-time event detection" (DED)…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…
A symbolic method is discussed which can be used to obtain the asymptotic bias and variance to order $O(1/n)$ for estimators in stationary time series. Using this method the bias to $O(1/n)$ of the Burg estimator in AR(1) and AR(2) models…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural notion of "degree" and a more general notion that we call "logexponential degree." Specifically,…