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On the application of the Minkowski‐Farkas theorem to sampling designs
Author(s) -
Akahira M.,
Takeuchi K.
Publication year - 1993
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1993.tb01418.x
Subject(s) - minkowski space , mathematics , sequence (biology) , unit (ring theory) , minkowski addition , sampling (signal processing) , minkowski's theorem , discrete mathematics , combinatorics , computer science , geometry , genetics , mathematics education , filter (signal processing) , computer vision , biology
In the paper, we consider the following problem: Let { π k } be a sequence satisfying 0π k Σ1 ( k= 1 ,…, N ) and π =n.Tben , is there an unordered sampling design such that, for each k =1,… N , the inclusion probability of unit k is equal to π? It is shown that it can be solved by the straightforward application of the Minkowski‐Farkas theorem.