Related papers: Gaussian model selection with an unknown variance

We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an…

In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…

Let $Y$ be a Gaussian vector of $\mathbb{R}^n$ of mean $s$ and diagonal covariance matrix $\Gamma$. Our aim is to estimate both $s$ and the entries $\sigma_i=\Gamma_{i,i}$, for $i=1,...,n$, on the basis of the observation of two independent…

We consider the problem of estimating the conditional mean of a real Gaussian variable $\nolinebreak Y=\sum_{i=1}^p\nolinebreak\theta_iX_i+\nolinebreak \epsilon$ where the vector of the covariates $(X_i)_{1\leq i\leq p}$ follows a joint…

A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…

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…

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…

A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…

We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…

We consider the classical problem of estimating a vector $\bolds{\mu}=(\mu_1,...,\mu_n)$ based on independent observations $Y_i\sim N(\mu_i,1)$, $i=1,...,n$. Suppose $\mu_i$, $i=1,...,n$ are independent realizations from a completely…

We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions…

For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…

The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time…

We consider the problem of estimating the means $\mu_i$ of $n$ random variables $Y_i \sim N(\mu_i,1)$, $i=1,\ldots ,n$. Assuming some structure on the $\mu$ process, e.g., a state space model, one may use a summary statistics for the…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…

Given data drawn from a collection of Gaussian variables with a common mean but different and unknown variances, what is the best algorithm for estimating their common mean? We present an intuitive and efficient algorithm for this task. As…

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models…

We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…