An Improved Result Relating Quadratic Forms and Chi-Square Distributions
Michael F. Driscoll · The American Statistician · 1999
Results from the theory of linear models establish a particular idempotency condition as being necessary and sufficient for a quadratic form in a nonsingular normal vector to follow a chi-square distribution. We give a theorem that is somewhat stronger than the standard ones, and provide a proof that is more accessible than those usually given, in that it uses only linear algebra and calculus.