B.S.T.J. Briefs: Estimation of the Variance of a Stationary GaussianRandom Process by Periodic Sampling

This paper* applies previous work 1 on estimation of the mean of a stationary random process by periodic sampling to estimation of the variance with the added restriction that the process under consideration be Gaussian with known mean. The samples are taken from a sample function of the random process, in a closed interval (0, T) and are in general correlated. The estimator used is the average of equally-weighted squared samples. The variance of this estimator is derived and its behavior is predicted as a function of the number of samples and length of record.