We present a general refinement of the Cauchy-Schwarz inequality over complete inner product spaces and show that it can be of interest for some statistical applications. This generalizes and simplifies previous results on the same subject.

翻译：本文提出了完全内积空间上柯西-施瓦茨不等式的一种一般性改进，并论证了该改进在若干统计应用中具有重要价值。该结果推广并简化了此前关于同一主题的研究结果。