Related papers: Nonparametric Shape-restricted Regression

Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…

We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

We construct confidence sets for the regression function in nonparametric binary regression with an unknown design density. These confidence sets are adaptive in $L^2$ loss over a continuous class of Sobolev type spaces. Adaptation holds in…

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

In constrained stochastic optimization, one naturally expects that imposing a stricter feasible set does not increase the statistical risk of an estimator defined by projection onto that set. In this paper, we show that this intuition can…

We present a general principle for estimating a regression function nonparametrically, allowing for a wide variety of data filtering, for example, repeated left truncation and right censoring. Both the mean and the median regression cases…

The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…

This paper considers the problem of estimating a periodic function in a continuous time regression model with a general square integrable semimartingale noise. A model selection adaptive procedure is proposed. Sharp non-asymptotic oracle…

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…

We consider a convex constrained Gaussian sequence model and characterize necessary and sufficient conditions for the least squares estimator (LSE) to be minimax optimal. For a closed convex set $K\subset \mathbb{R}^n$ we observe…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

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 note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…

In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…

Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…

Let $Y\in\R^n$ be a random vector with mean $s$ and covariance matrix $\sigma^2P_n\tra{P_n}$ where $P_n$ is some known $n\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or…