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We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
We propose a doubly robust estimator for the average treatment effect in high dimensional low sample size observational studies, where contamination and model misspecification pose serious inferential challenges. The estimator combines…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
Penalized likelihood methods with an $\ell_{\gamma}$-type penalty, such as the Bridge, the SCAD, and the MCP, allow us to estimate a parameter and to do variable selection, simultaneously, if $\gamma\in (0,1]$. In this method, it is…
We propose a sparse coefficient estimation and automated model selection procedure for autoregressive (AR) processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the…
It has been shown that AIC-type criteria are asymptotically efficient selectors of the tuning parameter in non-concave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is…
Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed…
Difficulties may arise when analyzing longitudinal data using mixed-effects models if there are nonparametric functions present in the linear predictor component. This study extends the use of semiparametric mixed-effects modeling in cases…
In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
A rich literature exists on constructing non-parametric estimators with optimal asymptotic properties. In addition to asymptotic guarantees, it is often of interest to design estimators with desirable finite-sample properties; such as…
Non-concave penalized maximum likelihood methods, such as the Bridge, the SCAD, and the MCP, are widely used because they not only do parameter estimation and variable selection simultaneously but also have a high efficiency as compared to…
We introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls…
Choosing a shrinkage method can be done by selecting a penalty from a list of pre-specified penalties or by constructing a penalty based on the data. If a list of penalties for a class of linear models is given, we provide comparisons based…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
The aim of this paper is to introduce an adaptive penalized estimator for identifying the true reduced parametric model under the sparsity assumption. In particular, we deal with the framework where the unpenalized estimator of the…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
This paper proposes a general framework for penalized convex empirical criteria and a new version of the Sparse-Group LASSO (SGL, Simon and al., 2013), called the adaptive SGL, where both penalties of the SGL are weighted by preliminary…