Joining models with commutative orthogonal block structure

Ela Commutative Orthogonal Block Structure and Error Orthogonal Models

A model has orthogonal block structure, OBS, if it has variance-covariance matrix that is a linear combination of known pairwise orthogonal orthogonal projection matrices that sum to the identity matrix. These models were introduced by Nelder is 1965, and continue to play an important part in randomized block designs. Two important types of OBS are related, and necessary and sufficient conditio...

Commutative orthogonal block structure and error orthogonal models

A model has orthogonal block structure, OBS, if it has variance-covariance matrix that is a linear combination of known pairwise orthogonal orthogonal projection matrices that sum to the identity matrix. These models were introduced by Nelder is 1965, and continue to play an important part in randomized block designs. Two important types of OBS are related, and necessary and sufficient conditio...

Monic Non-commutative Orthogonal Polynomials

For a measure μ on R, the situation is more subtle. One can always orthogonalize the subspaces of polynomials of different total degree (so that one gets a family of pseudo-orthogonal polynomials). The most common approach is to work directly with these subspaces, without producing individual orthogonal polynomials; see, for example [DX01]. One can also further orthogonalize the polynomials of ...

The Lattice Structure of Orthogonal Linear Models and Orthogonal Variance Component Models

On Orthogonal Block Elimination

We consider the block elimination problem Q A 1 A 2 = ?C 0 , where, given a matrix A 2 R mk , A 11 2 R kk , we try to nd a matrix C with C T C = A T A and an orthogonal matrix Q that eliminates A 2. Sun and Bischof recently showed that any orthogonal matrix can be represented in the so-called basis-kernel representation Q = Q(Y; S) = I ? Y ST T. Applying this framework to the block elimination ...