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Modelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are…
We introduce two variants of the information spectrum relative entropy defined by Tomamichel and Hayashi which have the particular advantage of satisfying the data-processing inequality, i.e. monotonicity under quantum operations. This…
We propose a nonparametric bootstrap procedure for two-phase stratified sampling without replacement. In this design, a weighted likelihood estimator is known to have smaller asymptotic variance than under the convenient assumption of…
The development of high-dimensional white noise test is important in both statistical theories and applications, where the dimension of the time series can be comparable to or exceed the length of the time series. This paper proposes…
This paper proposes a determined blind source separation method using Bayesian non-parametric modelling of sources. Conventionally source signals are separated from a given set of mixture signals by modelling them using non-negative matrix…
We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative…
The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…
Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…
We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…
We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the…
We investigate the problem of transforming an input sequence into a high-dimensional output sequence in order to transcribe polyphonic audio music into symbolic notation. We introduce a probabilistic model based on a recurrent neural…
In this monograph, we review recent advances in second-order asymptotics for lossy source coding, which provides approximations to the finite blocklength performance of optimal codes. The monograph is divided into three parts. In part I, we…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set…
We consider a multiterminal source coding problem in which a source is estimated at a central processing unit from lossy-compressed remote observations. Each lossy-encoded observation is produced by a remote sensor which obtains a noisy…
We propose a bootstrap procedure for data that may exhibit clustering in two or more dimensions. We use insights from the theory of generalized U-statistics to analyze the large-sample properties of statistics that are sample averages from…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve…
A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
In this paper, we employ asymptotic analysis to determine information about small volume defects in a known anisotropic scattering medium from far field scattering data. The location of the defects is reconstructed via the MUSIC algorithm…