Improved Estimators of High-Dimensional Expectation Vectors

Abstract

Until recently efforts to improve estimators of the expectation value vector were restricted to a special case of shrinkage estimators, that is, estimators with a scalar multiple of the sample mean [23], [25]. The distributions were assumed to be normal or centrally symmetric. In the previous chapter we considered component-wise estimators for vectors with independent components. Now we look for improved estimators of the expectation vectors for dependent variables. We start from an idea to shrink variables in a component-wise manner as in Chapter 6, but for approximately independent variables that are produced by passing to the system of coordinates, where the sample covariance matrix is diagonal. Thus the shrinkage coefficients will depend on the sample covariance matrix; we assume that they do not depend on any other variables including sample means.