Can the sample variance estimator be improved by using a covariate?

Abstract

Variance componentsare quantities of central interest in many applications, e.g., in cultivar yield stability analysis and in the analysis of measurement errors. In some applications, the feasible sample size is rather limited, leading to estimates of variance components that are subject to considerable sampling variation. For example, new crop cultivars are tested in only a few environments before release to the market, so the sample size for the variance across environments is small. Similarly, testing a new measurement instrument for some chemical compound may be costly, allowing only a limited number of replications. This article investigates the potential for improving the usual sample variance estimator by exploiting covariate information. In a cultivartrial, yield data may be available for only a few environments while meteorological data or data on a standard cultivar has been recorded for a very large number of environments. Likewise, in the analysis of measurement errors, there may be long-term data on a standard measurement procedure that can be used as a covariate to improve the variance estimate for a new instrument. It is shown in this article that the gain in accuracy achieved by using a covariate can be considerable, provided there is sufficient correlation between the covariate and the variable of interest.