Statistical Aspects of Estimated Principal Vectors (EOFs) Based on small Sample Sizes

Abstract

Statistical properties of estimated nonisotropic principal vectors [empirical orthogonal functions (EOFs)] are reviewed and discussed. The standard eigenvalue estimator is nonnormally distributed and biased: the largest one becomes overestimated, the smallest ones underestimated. Generally, the variance of the eigenvalue estimate is large. The standard eigenvalue estimator may be used to define an unbiased estimator, which, however, exhibits an increased variance. If a fixed set of EOFs is used, the FOF coefficients are not stochastically independent. The variances of the low-indexed coefficients become considerably overestimated by the respective estimated eigenvalues, those of the high-indexed coefficients underestimated. If the ratio of degrees of freedom to sample size is one-half or even less, these disadvantages are still current as is demonstrated by an example.