From: Bi-linear matrix-variate analyses, integrative hypothesis tests, and case-control studies
Step | Description |
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(1) | infer \(\tilde {\mathbf {s}}=I_{\textit {nf}}(X_{0}|| X_{1})\) in the multidimensional space of statistics s, where \(\tilde {\mathbf {s}}_{{X}_{1||0}}=I_{\textit {nf}}(X_{0}||X_{1})\) means that \(\tilde {\mathbf {s}}\) is inferred from the given sample set X _{0},X _{1} by an inferring method I _{ nf }, and the subscript X _{1||0} is used as the abbreviation of X _{1}||X _{0}, which will be used whenever its omission will not cause confusion. |
(2) | use \(\tilde {\mathbf {s}}\) to design an unbounded boundary that divides the space of statistics s into two separated and unbounded half-spaces. |
(3) | let the one that does not contain the origin 0 as the rejection domain \(\Gamma (\tilde {\mathbf {s}})\), with the corresponding boundary side named as the R-side. The other one is the acceptance domain. |
(4) | tend to reject H _{0} as s deviates from the R-side of boundary with a nonzero distance. The larger the distance is, the more seriously H _{0} breaks. |