The Concentration Ellipsoid of a Random Vector Revisited
综述了随机向量集中椭球的多种定义，提出Darmois定义的扩展作为最自然的选择，并用新证明展示其在简化线性估计理论证明中的优势。
Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation of a nonnegative definite quadratic form, together with the corresponding Cauchy-Schwarẓ-type inequality, is seen to play a crucial role in these proofs.