相关论文: A Structural Approach to Coordinate-Free Statistic…

This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers…

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via…

This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…

In this paper, we introduce structured sparsity estimators in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018) recently for fixed design and normal errors.…

We study the asymptotic properties of the adaptive Lasso in cointegration regressions in the case where all covariates are weakly exogenous. We assume the number of candidate I(1) variables is sub-linear with respect to the sample size (but…

In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature…

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…

The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…

It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…

Learning rates for least-squares regression are typically expressed in terms of $L_2$-norms. In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the…

A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…

When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects…

Linear regression using ordinary least squares (OLS) is a critical part of every statistician's toolkit. In R, this is elegantly implemented via lm() and its related functions. However, the statistical inference output from this suite of…

The recent thought-provoking paper by Hansen [2022, Econometrica] proved that the Gauss-Markov theorem continues to hold without the requirement that competing estimators are linear in the vector of outcomes. Despite the elegant proof, it…

We give the first tester-learner for halfspaces that succeeds universally over a wide class of structured distributions. Our universal tester-learner runs in fully polynomial time and has the following guarantee: the learner achieves error…

This paper introduces and analyzes a framework that accommodates general heterogeneity in regression modeling. It demonstrates that regression models with fixed or time-varying parameters can be estimated using the OLS and time-varying OLS…

A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…

We investigate multiple testing and variable selection using the Least Angle Regression (LARS) algorithm in high dimensions under the assumption of Gaussian noise. LARS is known to produce a piecewise affine solution path with change points…

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and…