Linear estimators for Gaussian random variables in Hilbert spaces

05/18/2023

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by   Stefan Tappe, et al.

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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. An application to Machine Learning is presented as well, namely we treat a linear regression problem in infinite dimensions.