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Linear estimators for Gaussian random variables in Hilbert spaces

Statistics Theory 2025-11-21 v2 Functional Analysis Probability Statistics Theory

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.

Keywords

Cite

@article{arxiv.2305.11083,
  title  = {Linear estimators for Gaussian random variables in Hilbert spaces},
  author = {Stefan Tappe},
  journal= {arXiv preprint arXiv:2305.11083},
  year   = {2025}
}

Comments

22 pages, 1 figure

R2 v1 2026-06-28T10:38:23.550Z