Non-central Cochran's Theorem for Elliptically Contoured Distributions

§1. Introduction The theory of the family of elliptically contoured distributions was established, when statis-ticians tried to extend classical sampling theory in multivariate analysis to the case of dependentsamples or non-normal samples. Recently, a great deal of attention has been paid to the theory ofelliptically contoured distributions. For a review, we refer to Fang kaitai (1984) or Chmieleswkt(1981). Although the basic theory of the elliptically contoured distributions tends to be more andmore perfect, a lot of work can be done in the area of its statistical applications. This paper extendsnon-central Cochran’s Theorem from normal distribution to ellipticacally contoured distributions.