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We introduce a methodology to test models with spatial variations of the fine-structure constant $\alpha$, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations…
In this study, we explore a robust testing procedure for the high-dimensional location parameters testing problem. Initially, we introduce a spatial-sign based max-type test statistic, which exhibits excellent performance for sparse…
Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a…
Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
This paper studies the properties of solutions for a double nonlinear time-dependent parabolic equation with variable density, not in divergence form with a source or absorption. The problem is formulated as a partial differential equation…
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…
We propose a two-sample test for covariance matrices in the high-dimensional regime, where the dimension diverges proportionally to the sample size. Our hybrid test combines a Frobenius-norm-based statistic as considered in Li and Chen…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
We consider change-point latent factor models for high-dimensional time series, where a structural break may exist in the underlying factor structure. In particular, we propose consistent estimators for factor loading spaces before and…
While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
The issue of combining individual $p$-values to aggregate multiple small effects is prevalent in many scientific investigations and is a long-standing statistical topic. Many classical methods are designed for combining independent and…
We consider the detection problem of correlations in a $p$-dimensional Gaussian vector, when we observe $n$ independent, identically distributed random vectors, for $n$ and $p$ large. We assume that the covariance matrix varies in some…
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…
This article deals with goodness-of-fit test for the Cauchy distribution. Some tests based on Kullback-Leibler information are proposed, and shown to be consistent. Monte Carlo evidence indicates that the tests have satisfactory…
This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…
Many scientific and engineering challenges -- ranging from pharmacokinetic drug dosage allocation and personalized medicine to marketing mix (4Ps) recommendations -- require an understanding of the unobserved heterogeneity in order to…