Related papers: Oracle Inequality for Instrumental Variable Regres…

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…

Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges, such as personalized medicine and optimal resource allocation. In this paper, we develop a general class of two-step algorithms for…

We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…

The authors study statistical linear inverse problems in Hilbert spaces. Approximate solutions are sought within a class of linear one-parameter regularization schemes, and the parameter choice is crucial to control the root mean squared…

In large-scale modern data analysis, first-order optimization methods are usually favored to obtain sparse estimators in high dimensions. This paper performs theoretical analysis of a class of iterative thresholding based estimators defined…

We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…

We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

We consider the problem of recovering an unknown vector from noisy data with the help of projection estimates. The goal is to find a convex combination of these estimates with the minimal risk. We study an aggregation method based on the…

In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and…

In a general counting process setting, we consider the problem of obtaining a prognostic on the survival time adjusted on covariates in high-dimension. Towards this end, we construct an estimator of the whole conditional intensity. We…

In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model…

We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…

The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general…

The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…

Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment or outcome. We first consider…

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…

Machine learning contrasts with traditional software development in that the oracle is the data, and the data is not always a correct representation of the problem that machine learning tries to model. We present a survey of the oracle…

Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…

We prove oracle inequalities for a penalized log-likelihood criterion that hold even if the data are not independent and not stationary, based on a martingale approach. The assumptions are checked for various contexts: density estimation…