Related papers: Minimax risks for sparse regressions: Ultra-high-d…

We derive non-asymptotic bounds for the minimax risk of variable selection under expected Hamming loss in the Gaussian mean model in $\mathbb{R}^d$ for classes of $s$-sparse vectors separated from 0 by a constant $a > 0$. In some cases, we…

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…

This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…

This paper considers the sample-efficiency of preference learning, which models and predicts human choices based on comparative judgments. The minimax optimal estimation error rate $\Theta(d/n)$ in classical estimation theory requires that…

We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection…

We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…

This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…

We determine the exact minimax rate of a Gaussian sequence model under bounded convex constraints, purely in terms of the local geometry of the given constraint set $K$. Our main result shows that the minimax risk (up to constant factors)…

We investigate the high-dimensional linear regression problem in the presence of noise correlated with Gaussian covariates. This correlation, known as endogeneity in regression models, often arises from unobserved variables and other…

We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…

This paper considers point and interval estimation of the $\ell_q$ loss of an estimator in high-dimensional linear regression with random design. We establish the minimax rate for estimating the $\ell_{q}$ loss and the minimax expected…

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other $\ell_r$ norms. Motivated…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…

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…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…

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…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…