On the Variance of Probability Estimates with Correlated Data
Robert R. Beland · 1982
Abstract : The foundations for probability estimation are presented for random processes in discrete time. The estimators considered are the empirical distribution function and the amplitude histogram and conditions are given for these to be unbiased and consistent. Expressions for the variance and covariance of these estimators are presented and the effect of correlations on these quantities is discussed and demonstrated numerically by simulations. A theorem establishes a monotonic relation between the variance and the correlation for Gaussian processes.