Delta method Slutsky Theorem

(I. Introduction

Recently, the sample survey method classes $ Delta $ and came back, and the teachers say and $ Slutsky $ theorems are very important, so finishing

(B) $ Slutsky $ Theorem

• Description: set $ X_n \ stackrel {d} {\ longrightarrow} X, Y_n \ stackrel {p} {\ longrightarrow} c $, where $ c $ is a constant, and $ g (x, y) $ in $ \ forall x \ in the support and set at $ y = c $ X $ continuous, then $ g (X_n, Y_n) \ stackrel {d} {\ longrightarrow} g (X, c) $