Related papers: Hypothesis Testing in High-Dimensional Regression …
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…
High-dimensional auto-regressive models provide a natural way to model influence between $M$ actors given multi-variate time series data for $T$ time intervals. While there has been considerable work on network estimation, there is limited…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…
Consider the case that we observe $n$ independent and identically distributed copies of a random variable with a probability distribution known to be an element of a specified statistical model. We are interested in estimating an infinite…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
Minimax $L_2$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$…
An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
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…
We consider a general model for high-dimensional empirical risk minimization whereby the data $\mathbf{x}_i$ are $d$-dimensional Gaussian vectors, the model is parametrized by $\mathbf{\Theta}\in\mathbb{R}^{d\times k}$, and the loss depends…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not strictly convex, and hence it may not have a…