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Table 6 S-space boundary based test (BBT)

From: Bi-linear matrix-variate analyses, integrative hypothesis tests, and case-control studies

Step Description
(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.