Show that for any r ≥ 1, S (r) n − S (0) n is positive semidefinite. What can you say about the rate of convergence (as n → ∞) of kS (r) n − S (0) n k ? In Chapters 4–6, second order asymptotic...

Show that for any r ≥ 1, S (r) n − S (0) n is positive semidefinite. What can you say about the rate of convergence (as n → ∞) of kS (r) n − S (0) n k ?

In Chapters 4–6, second order asymptotic representations were considered for M-, L-, and R-estimators. Can they be used to verify the Anscombe (1952) condition?