5
$\begingroup$

This image is from Applied Multivariate Analysis. In this image plim means convergence in probability. I could not find the reference about the statement for random matrices. I'd highly appreciate if you cite the reference or give the proof. Thanks

This

1 Answers 1

0

Random matrix is just a vector. Then you have joint distribution of $Y_n, X_n$ converges to $A,B$ where $A,B$ are independent. Continuous Mapping Theorem can be applied to conclude that for any continuous function $f(X_n,Y_n) \to f(X,Y)$.