Related papers: Nonparametric Least Squares Estimation of a Multiv…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares…
In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically…
Under the usual nonparametric regression model with Gaussian errors, Least Squares Estimators (LSEs) over natural subclasses of convex functions are shown to be suboptimal for estimating a $d$-dimensional convex function in squared error…
Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete…
We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…
This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been…
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…
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 propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex…
The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
We consider a nonparametric version of the integer-valued GARCH(1,1) model for time series of counts. The link function in the recursion for the variances is not specified by finite-dimensional parameters, but we impose nonparametric…