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On the asymptotic distribution of a class of aligned rank order test statistics in randomized block designs
Author(s) -
Tardif Serge
Publication year - 1980
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 - 10.2307/3314666
Subject(s) - mathematics , asymptotic distribution , statistics , equivalence (formal languages) , mathematical proof , rank (graph theory) , order statistic , combinatorics , quadratic equation , null hypothesis , class (philosophy) , statistical hypothesis testing , block (permutation group theory) , discrete mathematics , computer science , estimator , geometry , artificial intelligence
Abstract In the present investigation, the unconditional asymptotic distribution of a class of aligned rank order test statistics for randomized block designs is derived under the null hypothesis and for nearby alternatives, as the number of blocks tends to infinity. The proofs of these results are based on the asymptotic equivalence in quadratic mean between aligned observations and their ranks and thus are quite similar to the Hájek and SKidák (1967) approach.