ESTIMATING MEAN AND VARIANCE OF SUM OF CORRELATED RANDOM VARIABLES USING EMPIRICAL MOMENTS

This paper discusses three approaches to estimate the mean and the variance of sum of correlated random variables (SCRV), Z(N) = X-1 + X-2 + ... + X-N. The first approach is based on the empirical moments of SCRV, the second approach is based on the empirical moments of X-j's, and the third approach is based on the weighted mean of the sum of empirical moments of X-j's. Simulations are conducted to compare the performance of all approaches. The simulation results show that the first and the second approach have the same performance to estimate the mean of SCRV. The two approaches are more accurate than the second approach to estimate the mean of SCRV except for the distribution of N is uniform. When the distribution of N is uniform, the estimator of mean of SCRV for the second approach is more accurate than others. For large sample size (m = 1000), the estimator of variance of SCRV for the first approach is better than others.