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Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant | σ 2 | in the MGM model ( U , X B , σ 2 V ) , > 0 , scalar σ 2 > 0 , with a matrix V 0 . A known n × p random matrix U has the expected value E ( U ) = X B , where the n × d matrix X is a known matrix of an experimental design, B is an unknown d × p matrix of parameters and σ 2 V is the covariance matrix of U , being the symbol of the Kronecker...

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