The Cauchy-Schwartz inequality implies that the asymptotic variance of is:
A)greater than .
B)less than or equal to .
C)equal to .
D)less than .

Question

The Cauchy-Schwartz inequality implies that the asymptotic variance of ​  is:
A)​greater than . 
B)​less than or equal to . 
C)​equal to . 
D)​less than .

Quizplus · Accepted Answer

The Cauchy-Schwartz inequality states that for any two random variables X and Y,
$	ext{Cov}(X,Y)^2 \leq 	ext{Var}(X)	ext{Var}(Y)$
Thus, for the variables in question,
$	ext{Asymptotic variance of } \hat{	heta}_{1,n}^2 \leq 	ext{Asymptotic variance of }\hat{	heta}_{2,n}^2$
This means that the answer is B, the asymptotic variance of ​ $\hat{	heta}_{1,n}^2$ is less than or equal to the asymptotic variance of $\hat{	heta}_{2,n}^2$.

The Cauchy-Schwartz Inequality Implies That the Asymptotic Variance of ​

The Cauchy-Schwartz Inequality Implies That the Asymptotic Variance of