Estimation of Covariance Matrix
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چکیده
Estimation of population covariance matrices from samples of multivariate data is important. (1) Estimation of principle components and eigenvalues. (2) Construction of linear discriminant functions. (3) Establishing independence and conditional independence. (4) Setting confidence intervals on linear functions. Suppose we observed p dimensional multivariate samples X1, X2, · · · , Xn i.i.d. with mean 0 and covariance matrix Σp, and write Xi = (Xi1, Xi2, · · · , Xip)′. Our goal is to estimate Σp. For simplicity, we first consider the Gaussian case, where Xi ∼ N(0,Σp).
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