TY - JOUR
T1 - Barnard convex sets
AU - Almendra-Arao, Félix
PY - 2011/1
Y1 - 2011/1
N2 - In calculating significance levels for statistical non inferiority tests, the critical regions that satisfy the Barnard convexity condition have a central role. According to a theorem proved by Rohmel and Mansmann (1999), when the critical regions satisfy this condition, the significance level for non inferiority tests can be calculated much more efficiently. In this study, the sets that fulfil the Barnard convexity condition are called Barnard convex sets, and because of their relevance, we studied their properties independently of the context from which the sets originated. Among several results, we found that Barnard convex sets are a convex geometry and that each Barnard convex set has a unique basis. Also, we provide an algorithm for calculating the Barnard convex hull of any set. Finally, we present some applications of the concept of the Barnard convex hull of a set for non inferiority tests.
AB - In calculating significance levels for statistical non inferiority tests, the critical regions that satisfy the Barnard convexity condition have a central role. According to a theorem proved by Rohmel and Mansmann (1999), when the critical regions satisfy this condition, the significance level for non inferiority tests can be calculated much more efficiently. In this study, the sets that fulfil the Barnard convexity condition are called Barnard convex sets, and because of their relevance, we studied their properties independently of the context from which the sets originated. Among several results, we found that Barnard convex sets are a convex geometry and that each Barnard convex set has a unique basis. Also, we provide an algorithm for calculating the Barnard convex hull of any set. Finally, we present some applications of the concept of the Barnard convex hull of a set for non inferiority tests.
KW - Asymptotic test
KW - Barnard convex sets
KW - Barnard convexity condition
KW - Convex hull
KW - Non inferiority tests
UR - http://www.scopus.com/inward/record.url?scp=79956110382&partnerID=8YFLogxK
U2 - 10.1080/03610926.2010.484155
DO - 10.1080/03610926.2010.484155
M3 - Artículo
SN - 0361-0926
VL - 40
SP - 2574
EP - 2582
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 14
ER -