New answers tagged

1 vote

$X_n$ converges to $X$ in distribution. $Y_n$ converges to $Y$ in probability. Does $(X_n, Y_n)$ converges to $(X,Y)$ in distribution?

While this is wrong in general as per Zhanxiong's answer, it holds true if $Y$ is almost surely constant. I.e. If $X_n \overset{d}\to X$ and $Y_n \overset{p}\to c$, then $(X_n, Y_n)\overset{d}\to (X, ...
Felix B.'s user avatar
  • 111

Top 50 recent answers are included