An experiment produces a zero mean gaussian random vector

Reference no: EM131084008

An experiment produces a zero mean Gaussian random vector X = [X₁ ··· X_k] 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

(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 R_ij . That is, show that for any c > 0,

Reference no: EM131084008

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