Finally, we define a kXk matrix of second-order parameter estimates, S [Pg.205]

The matrix 9S(r)/90 contains the sensitivities of the second order responses with respect to the seismic parameters, with which the increase of the statistical moments due to the parameters spread can be estimated. However, perturbation methods in general are accurate only for parameters having a coefficient of variation of, say, less than 0.1. Since all the seismic parameters considered herein have a much larger spread, this technique should be discarded. [Pg.522]

The single-factor second-order parameter estimates lie along the diagonal of the S matrix, and the two-factor interaction parameter estimates are divided in half on either side of the diagonal. [Pg.255]

The rank of the matrix X is equal to k, and k < n. The first part of this assumption ensures that k variables are linearly independent. The second part requires that the number of observations exceeds the number of parameters to be estimated. This is essential in order to have the necessary degrees of freedom for parameter estimation. [Pg.478]

The quadratic model (Eq.3.3) allowed the generation of the 3-D response surface image (Fig. 3.5) for the main interaction between injection time and voltage. The quadratic terms in this equation models the curvature in the true response function. The shape and orientation of the curvature results from the eigenvalue decomposition of the matrix of second-order parameter estimates. After the parameters are estimated, critical values for the factors in the estimated surface can be found. For this study, a post hoc review of our model [Pg.84]

See also in sourсe #XX -- [ Pg.205 ]

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