Linear Models

Abstract

1.2 BLUEs Definition 1. Given a random sample, Y1, . . . , Yn ind ∼ f(X,β); an estimator β̂(Y1, . . . , Yn) of the parameter β is said to be unbiased if E[β̂|X] = β, for every β ∈ Rp . Definition 2. An estimator β̂ of a parameter β is said to be Best Linear Unbiased Estimator (BLUE), if it is a linear function of the observed values y, an unbiased estimator of β; and if for any other linear unbiased estimator β̃, we have Var[β̂|X] ≤ Var[β̃|X].