This paper presents null hypothesis distribution theory for certain methods of significance testing applicable to multivariate data. This theory is derived in Sections 2 and 3 using simple geometrical reasoning. Section 3 derives theory related to stepwise methods in a form sufficiently general to include both the standard methods of Section 4 and certain new methods based on principal variables of Section 5. The generality in Section 3 is made possible by the independence results proved in Section 2.
"Multivariate Theory for General Stepwise Methods." Ann. Math. Statist. 34 (3) 873 - 883, September, 1963. https://doi.org/10.1214/aoms/1177704010