Slutsky's theorem

If X_n converges in distribution to X and Y_n converges in probability to a constant c, then X_n + Y_n ⇒ X + c and X_n · Y_n ⇒ c · X (and X_n / Y_n ⇒ X/c if c ≠ 0). Slutsky 1925. Licenses plug-in variance estimators: studentised…