Determining the Stability of a Mean Estimate from Correlated Samples by Use of Linear Prediction

摘要

When a collection of N data samples of a stationary process are taken, a common method of estimating the mean of the random process is to use the sample mean of the available data. If the data samples are taken with a time increment large enough that they are linearly independent of each other, that is uncorrelated samples, then the variance of the mean estimate is equal to the actual (unknown) variance of the process divided by N. In this case, the quality of the mean estimate can be approximated by also estimating the process variance, that is, by computing the sample variance of the available data. However, when the time increment is small enough that the data samples are statistically dependent on each other, the variance of the mean estimate depends on the (unknown) covariance of the given process. Thus, in order to determine the stability of a first-order statistic (mean), we need information on a second-order statistic (covariance or spectrum). Since this latter information is unknown, we also need to estimate it from the available data. Three procedures for accomplishing this goal will be discussed here.