The Covariance Matrix of the Error Vector

Abstract

Assumption (iv) of the linear regression model claims the covariance matrix of the error vector ɛ to be Cov(ɛ) = σ²I_n with an unknown parameter σ² ∈ (0, ∞). This chapter discusses the estimation of σ² in detail, and introduces situations under which it appears to be reasonable to extend assumption (iv) to Cov(ε) = σ²V for some symmetric positive/nonnegative definite matrix V ≠ I _n