Simultaneous estimation of log-normal coefficients of variation: Shrinkage and pretest strategies

In this paper, we consider the problem of estimating the log-normal coefficients of variation when multiple samples from log-normal populations with unequal variances are combined. We suggest some efficient estimation methods based on pretest and JamesStein procedures. In a large-sample setup, we propose a test statistic (pretest) for testing the homogeneity assumption of log-normal coefficients of variation. Under a class of local alternatives, we obtain some asymptotic distributions to make fair comparisons of the suggested estimators based on asymptotic quadratic bias and risk. In addition, we conduct a Monte-Carlo simulation study to validate the relative efficiency performance of the proposed estimators when the homogeneity hypothesis may or may not hold. Unlike the pooled estimate of common coefficient of variation, the results show that James-Stein estimators behave robustly against departures from the homogeneity hypothesis and have bounded quadratic bias and risk. The results also show that the pretest estimators perform efficiently in a significant portion of the parameter space. Historical weather data is used to in the application of the proposed estimators.