Related papers: Adaptive estimation in regression models for weakl…
We consider the problem of adaptive estimation of the regression function in a framework where we replace ergodicity assumptions (such as independence or mixing) by another structural assumption on the model. Namely, we propose adaptive…
We study the estimation of quadratic Sobolev-type integral functionals of an unknown density on the unit sphere. The functional is defined through fractional powers of the Laplace--Beltrami operator and provides a global measure of…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown…
We consider the problem of estimating the value l({\phi}) of a linear functional, where the structural function {\phi} models a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of…
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
In this article we study the asymptotic predictive optimality of a model selection criterion based on the cross-validatory predictive density, already available in the literature. For a dependent variable and associated explanatory…
An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…
We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of…
This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…
Estimating causal effects from observational data informs us about which factors are important in an autonomous system, and enables us to take better decisions. This is important because it has applications in selecting a treatment in…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
Given an i.i.d. sample from a distribution $F$ on $\mathbb{R}$ with uniformly continuous density $p_0$, purely data-driven estimators are constructed that efficiently estimate $F$ in sup-norm loss and simultaneously estimate $p_0$ at the…
In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a…