Related papers: Computable error bounds for high-dimensional Edgew…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…
This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…
Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols.…
This paper considers testing a covariance matrix $\Sigma$ in the high dimensional setting where the dimension $p$ can be comparable or much larger than the sample size $n$. The problem of testing the hypothesis $H_0:\Sigma=\Sigma_0$ for a…
This paper reexamines the seminal Lagrange multiplier test for cross-section independence in a large panel model where both the number of cross-sectional units n and the number of time series observations T can be large. The first…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
We investigate the likelihood ratio test for a large block-diagonal covariance matrix with an increasing number of blocks under the null hypothesis. While so far the likelihood ratio statistic has only been studied for normal populations,…
This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be…
In this paper, we establish the Central Limit Theorem (CLT) for linear spectral statistics (LSSs) of large-dimensional generalized spiked sample covariance matrices, where the spiked eigenvalues may be either bounded or diverge to infinity.…
We study the renormalized real sample covariance matrix $H=X^TX/\sqrt{MN}-\sqrt{M/N}$ with $N/M\rightarrow0$ as $N, M\rightarrow \infty$ in this paper. And we always assume $M=M(N)$. Here $X=[X_{jk}]_{M\times N}$ is an $M\times N$ real…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
While batching methods have been widely used in simulation and statistics, it is open regarding their higher-order coverage behaviors and whether one variant is better than the others in this regard. We develop techniques to obtain…
Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case [W. Auzinger and…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…
In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…
The present paper considers testing an Erdos--Renyi random graph model against a stochastic block model in the asymptotic regime where the average degree of the graph grows with the graph size n. Our primary interest lies in those cases in…