Work

Linear estimators for Gaussian random variables in Hilbert spaces

Year: 2025

Type: article

Abstract: 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 confidence intervals and perform hypothesis testing. A linear regression problem in infinite dimensions and some perspectives to statistical and machine learning are presented as well.

Source: Theory of Probability and Mathematical Statistics

DOI: 10.1090/tpms/1230

Author: Stefan Tappe

Institution: University of Freiburg

Language: English

Topic: Advanced Statistical Methods and Models

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Award: Invarianzprobleme für stochastische partielle Differentialgleichungen