Related papers: To ignore dependencies is perhaps not a sin

Distributionally robust offline reinforcement learning (RL), which seeks robust policy training against environment perturbation by modeling dynamics uncertainty, calls for function approximations when facing large state-action spaces.…

Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…

We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order $d/n$ in dimension $d$ with $n$ samples. Here, we study…

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or…

We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of…

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

In the presence of a missing response, reweighting the complete case subsample by the inverse of nonmissing probability is both intuitive and easy to implement. When the population totals of some auxiliary variables are known and when the…

In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…

Under the usual nonparametric regression model with Gaussian errors, Least Squares Estimators (LSEs) over natural subclasses of convex functions are shown to be suboptimal for estimating a $d$-dimensional convex function in squared error…

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features.…

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…

We consider the problem of estimating an unknown $n_1 \times n_2$ matrix $\mathbf{\theta^*}$ from noisy observations under the constraint that $\mathbf{\theta}^*$ is nondecreasing in both rows and columns. We consider the least squares…

In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a…

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Deep learning research has uncovered the phenomenon of benign overfitting for overparameterized statistical models, which has drawn significant theoretical interest in recent years. Given its simplicity and practicality, the ordinary least…

In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…