Tag Archives: portmanteau theorem

Statement: $X_n \overset{D}{\to} X$ iff $E[g(X_n)] \to E[g(X)]$ for any bounded, continuous Lipschitz g. We prove this in two parts: Part 1 Here we show $X_n \overset{D}{\to} X$ implies $E[g(X_n)] \to E[g(X)]$ for any continuous bounded g. Let $F_n$ denote the cdf … Continue reading →