Related papers: Adaptive estimation of linear functionals in funct…

We consider the nonparametric regression with a random design model, and we are interested in the adaptive estimation of the regression at a point $x\_0$ where the design is degenerate. When the design density is $\beta$-regularly varying…

We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners…

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…

We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…

This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…

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…

We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the…

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…

We consider the problem of adaptive estimation of the functional component in a multivariate partial linear model where the argument of the function is defined on a $q$-dimensional grid. Obtaining an adaptive estimator of this functional…

We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…

In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem and can be solved using a…

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1} \mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance matrix…

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

We consider the model $Z_i=X_i+\varepsilon_i$, for i.i.d. $X_i$'s and $\varepsilon_i$'s and independent sequences $(X_i)_{i\in{\mathbb{N}}}$ and $(\varepsilon_i)_{i\in{\mathbb{N}}}$. The density $f_{\varepsilon}$ of $\varepsilon_1$ is…