Related papers: Estimator selection in the Gaussian setting

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…

We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…

This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of…

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

We introduce a new method for estimating the mean of an outcome variable within groups when researchers only observe the average of the outcome and group indicators across a set of aggregation units, such as geographical areas. Existing…

A general method to combine several estimators of the same quantity is investigated. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained…

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some…

Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often…

Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…

Aggregating estimators using exponential weights depending on their risk appears optimal in expectation but not in probability. We use here a slight overpenalization to obtain oracle inequality in probability for such an explicit…

Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…

We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…