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.

翻译：我们研究一类含未知参数的无穷维高斯随机变量的统计模型。针对该模型，我们推导了高斯分布均值与方差的线性估计量。进一步地，我们构建了置信区间并进行了假设检验。此外，本文还展示了该模型在机器学习中的应用——具体处理了无穷维空间中的线性回归问题。