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A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP). The disturbance covariance matrix should be inferred from training sample observations in practice. Large…
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…
We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a…
New tests are developed for two-way ANOVA models with heterogeneous error variances. The testing problems are considered for testing the significant interaction effects, simple effects, and treatment effects. The likelihood ratio tests…
In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…
This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use,…
One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…
Large language models (LLMs) are increasingly used in statistical research and applications. However,they are also notorious for unreliable or biased information. Here, we explore whether LLMs can be used to improve the precision of…
We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in…
In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…
Generalized linear mixed models (GLMM) are commonly used to analyze clustered data, but when the number of clusters is small to moderate, standard statistical tests may produce elevated type I error rates. Small-sample corrections have been…
In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature:…
This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…