Theory of Probability and Mathematical Statistics
Linear estimators for Gaussian random variables in Hilbert spaces
Stefan Tappe
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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: Gaussian random variable in a Hilbert space, statistical model, linear estimator, confidence interval, hypothesis testing, linear regression, statistical and machine learning
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