Related papers: $L^2$ Asymptotics for High-Dimensional Data
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…
In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…
\cite{HillMotegi2017} present a new general asymptotic theory for the maximum of a random array $\{\mathcal{X}_{n}(i)$ $:$ $1$ $\leq $ $i$ $\leq $ $\mathcal{L}\}_{n\geq 1}$, where each $\mathcal{X}_{n}(i)$ is assumed to converge in…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish…
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…
This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for…
Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime,…
We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…
In this paper, we discuss tests for mean vector of high-dimensional data when the dimension $p$ is a function of sample size $n$. One of the tests, called the decomposite $T^{2}$-test, in the high-dimensional testing problem is constructed…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
For the multi-sample equal covariance function (ECF) testing problem, Zhang (2013) proposed an $L^{2}$-norm based test. However, its asymptotic power and finite sample performance have not been studied. In this paper, its asymptotic power…
In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…
The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our main focus is on the two-dimensional case. Asymptotic upper…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…