Evaluating two methods of estimating error variances using simulated data sets with known errors

Abstract

In this paper we compare two different methods of estimating the error variances of two or more independent data sets. One method, called the "three-cornered hat" (3CH) method, requires three data sets. Another method, which we call the "two-cornered hat" (2CH) method, requires only two data sets. Both methods have been used in previous studies to estimate the error variances associated with a number of physical and geophysical data sets. A key assumption in both methods is that the errors of the data sets are not correlated, although some studies have considered the effect of the partial correlation of representativeness errors in two or more of the data sets. We compare the 3CH and 2CH methods using a simple model to simulate three and two data sets with various error correlations and biases. With this model, we know the exact error variances and covariances, which we use to assess the accuracy of the 3CH and 2CH estimates. We examine the sensitivity of the estimated error variances to the degree of error correlation between two of the data sets as well as the sample size. We find that the 3CH method is less sensitive to these factors than the 2CH method and hence is more accurate. We also find that biases in one of the data sets has a minimal effect on the 3CH method, but can produce large errors in the 2CH method.