Suppose that the regression model is y , where has a zero mean, constant variance, and equal correlation across observations Then Cov i, j 2 if i j Prove that the least squares estimator of is inconsistent Find the characteristic roots of and show that Condition 2 after Theorem 10 2 is violated ...

The covariance matrix is 0020 1 p p 1 1 E n P P LP 1 The matrix X is a column of ...

Suppose that the regression model is y = + , where has a zero mean,

Question:

Suppose that the regression model is y = μ + ε, where ε has a zero mean, constant variance, and equal correlation ρ across observations. Then Cov [εi, εj] = σ2ρ if i ≠ j . Prove that the least squares estimator of μ is inconsistent. Find the characteristic roots of Ω and show that Condition 2 after Theorem 10.2 is violated.