Reference no: EM131084075
X is 10-dimensional Gaussian (0,I) random vector. Since X is zero mean, RX = CX = I. We will use the method of Problem 7.3.7 and estimate RX using the sample correlation matrix
![](https://test.transtutors.com/qimg/71181c8c-3d0f-45b6-8286-066b1139adcf.png)
For n ∈ {10, 100, 1000, 10,000}, construct a Matlab simulation to estimate
![](https://test.transtutors.com/qimg/4696f1e5-9938-48f1-a41f-8d16eee47a97.png)
Problem 7.3.7
An experiment produces a zero mean Gaussian random vector X = [X1 ··· Xk] with correlation matrix R = E[XX']. To estimate R, we perform n independent trials, yielding the iid sample vectors X(1), X(2), . . . , X(n), and form the sample correlation matrix
![](https://test.transtutors.com/qimg/1e42db47-2093-49f9-b3fe-b07887bff63f.png)
(a) Show
(n) is unbiased by showing E[
(n)] = R.
(b) Show that the sequence of estimates
(n)is consistent by showing that every element
ij(n) of the matrix
converges to Rij . That is, show that for any c > 0,
![](https://test.transtutors.com/qimg/e3e8aaae-0d25-4c25-8c64-270b766dbddd.png)