Small samples estimation of dispersion effects from unreplicated data

Abstract

We compare the performance of three methods for identifying dispersion effects from unreplicated data: (1) Two-step estimation procedure -TSP- (Harvey 1976), (2) Iterated weighted least squares procedure -IWLS- and (3) Maximum likelihood estimation procedure -ML- (Harvey 1976). We conclude that small sample size estimators are biased: the IWLS and ML methods tend to amplify the absolute value of the real dispersion effect, whereas the TSP estimator tends to reduce it. Asymptotic expressions notably underestimate the IWLS's and ML's real variances. Finally, although ML is the most efficient with large samples, the simplest estimator, TSP, turns out as the most advisable choice with small sample sizes. A linear combination of TSP and ML, as an approximately unbiased dispersion effect estimator, AVEMT, is proposed. Three examples are discussed to illustrate the results.