Orthogonalization–Triangularization Methods in Statistical Computations

Abstract

Procedures are presented for reducing a data matrix to triangular form by using orthogonal transformations. It is shown how an analysis of variance can be constructed from the triangular reduction of the data matrix. Procedures for calculating sums of squares, degrees of freedom, and expected mean squares are presented. It is demonstrated that all statistics needed for inference on linear combinations of parameters of a linear model may be calculated from the triangular reduction of the data matrix.

Key Words:

• Orthogonalization
• Triangular reduction
• Analysis of variance
• Expected mean squares
• Linear combinations
• Estimability