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Testing multivariate uniformity: The distance‐to‐boundary method
Author(s) -
Berrendero José R.,
Cuevas Antonio,
Vjosázquezgrande Francisco
Publication year - 2006
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 - 10.1002/cjs.5550340409
Subject(s) - curse of dimensionality , test statistic , monte carlo method , range (aeronautics) , computer science , statistic , boundary (topology) , adaptability , algorithm , simplicity , multivariate statistics , statistical hypothesis testing , mathematics , point (geometry) , statistics , mathematical optimization , mathematical analysis , ecology , materials science , philosophy , geometry , epistemology , composite material , biology
Given a random sample taken on a compact domain S ⊂ d , the authors propose a new method for testing the hypothesis of uniformity of the underlying distribution. The test statistic is based on the distance of every observation to the boundary of S . The proposed test has a number of interesting properties. In particular, it is feasible and particularly suitable for high dimensional data; it is distribution free for a wide range of choices of 5; it can be adapted to the case that the support of S is unknown; and it also allows for one‐sided versions. Moreover, the results suggest that, in some cases, this procedure does not suffer from the well‐known curse of dimensionality. The authors study the properties of this test from both a theoretical and practical point of view. In particular, an extensive Monte Carlo simulation study allows them to compare their methods with some alternative procedures. They conclude that the proposed test provides quite a satisfactory balance between power, computational simplicity, and adaptability to different dimensions and supports.