Introduction to Asymptotic Theory Definition 4.1 [Convergence in Mean Squares (or in Quadratic Mean)]A sequence of random variables/vectors/matrices Zn,n=1,2,...,is said to converge to Z in mean squares as n->oo if ElZm-Z2→0asn→o, where is the sum of the absolute value of each component in Zn -Z. When Zn is a vector or a matrix,convergence can be understood as con- vergence in each element of Zn.When Zn-Z is a l x m matrix,where l and m are fixed positive integers,we can also define the squared norm as Z-Z2=∑∑Zm-☑ t=1s=1 Note that 2n converges to 2 in mean squares if and only if each component of Zn converges to the corresponding component of Z in mean squares. ADVANCED ECONOMETRICS Linear Regression Models with IID Observations March 31,2021 5ADVANCED ECONOMETRICS Linear Regression Models with IID Observations March 31, 2021 5 Introduction to Asymptotic Theory Definition 4.1