Related papers: Asymptotics and statistical inferences on independ…
We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of $X$, which, in the…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal intersection length against a fixed regular reference surface.…
We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
This paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix $\Gamma^{(m)}$ is dimension-dependent. Hence, by contrast with…
We compute the limiting distributions of the lengths of the longest monotone subsequences of random (signed) involutions with or without conditions on the number of fixed points (and negated points) as the sizes of the involutions tend to…
The max-stable H\"usler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We study the asymptotic laws for the spatial distribution and the number of connected components of zero sets of smooth Gaussian random functions of several real variables. The primary examples are various Gaussian ensembles of real-valued…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two…
We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R\to R is an unknown smooth function and X(t) is a real-valued stationary…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…