Related papers: M-type penalized splines with auxiliary scale esti…
Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of…
In this paper we propose a model selection approach to fit a regression model using splines with a variable number of knots. We introduce a penalized criterion to estimate the number and the position of the knots where to anchor the splines…
Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator,…
Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The…
Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…
Splines are useful building blocks when constructing priors on nonparametric models indexed by functions. Recently it has been established in the literature that hierarchical priors based on splines with a random number of equally spaced…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the…
The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…
The least trimmed squares (LTS) estimator is a renowned robust alternative to the classic least squares estimator and is popular in location, regression, machine learning, and AI literature. Many studies exist on LTS, including its…
The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
This text is the rejoinder following the discussion of a survey paper about minimal penalties and the slope heuristics (Arlot, 2019. Minimal penalties and the slope heuristics: a survey. Journal de la SFDS). While commenting on the remarks…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…
Markov-switching models are powerful tools that allow capturing complex patterns from time series data driven by latent states. Recent work has highlighted the benefits of estimating components of these models nonparametrically, enhancing…