Structured dispersion and validity in linear inference Original Research Article

Structured matrices image arise in nonstandard linear models, where e′ = [1, …, 1], γ′ = [γ1, …, γn], and image. Their properties are studied, including expressions for eigenvalues, conditions for positive definiteness, and conditioning of bE(γ) as γ varies. It is shown that if γ majorizes γ0, then the condition numbers are ordered as cφ(∑(γ)) greater-or-equal, slanted cφ(∑(γ0)) for every condition number {cφ(·); φ set membership, variant varrho} generated by the unitarily invariant matrix norms. Applications are noted in linear inference and in outlier detection.