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Related papers: Gaussian model selection with an unknown variance

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This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

Methodology · Statistics 2020-06-18 Georgios Papageorgiou , Benjamin C. Marshall

The estimation of the generalization error of classifiers often relies on a validation set. Such a set is hardly available in few-shot learning scenarios, a highly disregarded shortcoming in the field. In these scenarios, it is common to…

With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the non-linearity in data become more and more popular nowadays. It is often the case…

Applications · Statistics 2023-09-11 Zhiyong Hu , Dipak Dey

Consider the setting where there are B>1 candidate statistical models, and one is interested in model selection. Two common approaches to solve this problem are to select a single model or to combine the candidate models through model…

Methodology · Statistics 2021-04-22 Qingying Zong , Jonathan R. Bradley

Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probability that the output belongs to a specific region remains…

Applications · Statistics 2025-07-25 Romain Ait Abdelmalek-Lomenech , Julien Bect , Emmanuel Vazquez

When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…

Data Analysis, Statistics and Probability · Physics 2020-07-21 Giovanni Mana , Enrico Massa , Maria Predescu

We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family…

Statistics Theory · Mathematics 2007-12-18 Felix Abramovich , Vadim Grinshtein , Marianna Pensky

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…

Statistics Theory · Mathematics 2009-09-11 Ikhlef Bechar

We consider here estimation of an unknown probability density s belonging to L2(mu) where mu is a probability measure. We have at hand n i.i.d. observations with density s and use the squared L2-norm as our loss function. The purpose of…

Statistics Theory · Mathematics 2013-01-22 Lucien Birgé

We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that…

Statistics Theory · Mathematics 2017-02-03 Gábor Lugosi , Shahar Mendelson

We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our…

Methodology · Statistics 2026-02-25 Yixiang Luo , William Fithian , Lihua Lei

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,…

Statistics Theory · Mathematics 2019-07-30 Michael Law , Ya'acov Ritov

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…

Methodology · Statistics 2024-11-26 Tathagata Basu , Matthias C. M. Troffaes

We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…

Statistics Theory · Mathematics 2025-11-21 Stefan Tappe

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…

Methodology · Statistics 2026-05-01 Cory McCartan , Shiro Kuriwaki

We observe a random measure $N$ and aim at estimating its intensity $s$. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random…

Statistics Theory · Mathematics 2009-05-12 Yannick Baraud

This paper focuses on variable selection for a partially linear single-index varying-coefficient model. A regularized variable selection procedure by combining basis function approximations with SCAD penalty is proposed. It can…

Statistics Theory · Mathematics 2024-12-19 Lijuan Han , Liugen Xue , Junshan Xie

In this paper, we propose a maximum margin classifier that deals with uncertainty in data input. More specifically, we reformulate the SVM framework such that each training example can be modeled by a multi-dimensional Gaussian distribution…

Machine Learning · Computer Science 2017-11-21 Christos Tzelepis , Vasileios Mezaris , Ioannis Patras

Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…

Methodology · Statistics 2024-10-16 J. E. Griffin

The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…

Statistics Theory · Mathematics 2025-12-19 Yury A Kutoyants