Related papers: A Two-Stage Penalized Least Squares Method for Con…

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…

We consider a two-stage estimation method for linear regression. First, it uses the lasso in Tibshirani (1996) to screen variables and, second, re-estimates the coefficients using the least-squares boosting method in Friedman (2001) on…

This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…

Penalized least squares methods are commonly used for simultaneous estimation and variable selection in high-dimensional linear models. In this paper we compare several prevailing methods including the lasso, nonnegative garrote, and SCAD…

We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…

We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…

Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to…

We study the problem of high-dimensional variable selection via some two-step procedures. First we show that given some good initial estimator which is $\ell_{\infty}$-consistent but not necessarily variable selection consistent, we can…

We propose a novel estimation procedure for models with endogenous variables in the presence of spatial correlation based on Eigenvector Spatial Filtering. The procedure, called Moran's $I$ 2-Stage Lasso (Mi-2SL), uses a two-stage Lasso…

Penalised estimation methods for point processes usually rely on a large amount of independent repetitions for cross-validation purposes. However, in the case of a single realisation of the process, existing cross-validation methods may be…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…

As longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (e.g. sustained treatment strategies). In settings such as this, the preferred analysis…

This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions. We introduce a two-phase approach. The first phase…

We propose a penalized method for the least squares estimator of a multivariate concave regression function. This estimator is formulated as a quadratic programming (QP) problem with $O(n^2)$ constraints, where n is the number of…

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with…

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…

We aim to develop a time series modeling methodology tailored to high-dimensional environments, addressing two critical challenges: variable selection from a large pool of candidates, and the detection of structural break points, where the…

We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…