Related papers: Asymptotic variance of grey-scale surface area est…
We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean…
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 extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbour balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the…
In this paper, we provide $R$-estimators of the location of a rotationally symmetric distribution on the unit sphere of $\R^k$. In order to do so we first prove the local asymptotic normality property of a sequence of rotationally symmetric…
In this paper we consider the convex hull of a spherically symmetric sample in $R^d$. Our main contributions are some new asymptotic results for the expectation of the number of vertices, number of facets, area and the volume of the convex…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…
Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…
We construct uniform and point-wise asymptotic confidence sets for the single edge in an otherwise smooth image function which are based on rotated differences of two one-sided kernel estimators. Using methods from M-estimation, we show…
We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the extent to which the high…
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the…
In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two…
In this paper, we study the asymptotic properties (bias, variance, mean squared error) of Bernstein estimators for cumulative distribution functions and density functions near and on the boundary of the $d$-dimensional simplex. Our results…
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…
Following Wiener, we consider the zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We show that the variance of the number of zeroes in a long horizontal rectangle $[0,T]\times…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
This paper addresses the asymptotic performance of popular spatial regression estimators of the linear effect of an exposure on an outcome under ``spatial confounding" -- the presence of an unmeasured spatially-structured variable…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…
We show that nonparametric regression is asymptotically equivalent in Le Cam's sense with a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework based on…