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Testing independence with additional information
Author(s) -
Perron François
Publication year - 1991
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315540
Subject(s) - dimension (graph theory) , independence (probability theory) , combinatorics , independent and identically distributed random variables , multinomial distribution , mathematics , invariant (physics) , discrete mathematics , random variable , statistics , mathematical physics
Let X = (X j : j = 1,…, n) be n row vectors of dimension p independently and identically distributed multinomial. For each j, X j is partitioned as X j = (X j 1 , X j 2 , X j 3 ), where p i is the dimension of X j i with p 1 = 1, p 1 + p 2 + p 3 = p . In addition, consider vectors Y j i , i = 1,2j = 1,…, n i that are independent and distributed as X 1 i . We treat here the problem of testing independence between X 1 1 and X 1 3 knowing that X 1 1 and X 1 2 are uncorrected. A locally best invariant test is proposed for this problem.