Related papers: Degrees of Freedom for Piecewise Lipschitz Estimat…

In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…

This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is…

Two extensions of generalized linear models are considered. In the first one, response variables depend on multiple linear combinations of covariates. In the second one, only response variables are observed while the linear covariates are…

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…

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the…

Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Although most of the estimators claim to be the maximum likelihood estimators, the claim is only partially true since the…

We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…

This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…

We propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the $\ell_\infty$ estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a…

Estimation methods for the L\'{e}vy density of a L\'{e}vy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good…

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first-…

Recently emerging large-scale biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors in the data may create difficulties in estimation. There are…

The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…

The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…

Sparse model selection by structural risk minimization leads to a set of a few predictors, ideally a subset of the true predictors. This selection clearly depends on the underlying loss function $\tilde L$. For linear regression with square…

Estimators derived from score functions that are not the likelihood are in wide use in practical and modern applications. Their regularization is often carried by pseudo-posterior estimation, equivalently by adding penalty to the score…

The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…

We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are…

Recent research has focused on $\ell_1$ penalized least squares (Lasso) estimators for high-dimensional linear regressions in which the number of covariates $p$ is considerably larger than the sample size $n$. However, few studies have…

In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…