Related papers: On Minimax Exponents of Sparse Testing

In the high dimensional regression analysis when the number of predictors is much larger than the sample size, an important question is to select the important variable which are relevant to the response variable of interest. Variable…

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…

The proportional hazards model has been extensively used in many fields such as biomedicine to estimate and perform statistical significance testing on the effects of covariates influencing the survival time of patients. The classical…

We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…

This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…

The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…

We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…

Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…

Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…

We consider the problem of detection of sparse anomalies when monitoring a large number of data streams continuously in time. This problem is addressed using anytime-valid tests. In the context of a normal-means model and for a fixed…

We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the asymptotic bias of this algorithm at small step-sizes and…

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to $b$ bits. We investigate both the $d$- and infinite-dimensional signal…

This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…