Circular Likelihood Ratio Tests for the Main Problem

  • Johan C. Akkerboom
Part of the Lecture Notes in Statistics book series (LNS, volume 62)


In the present chapter we discuss some ways in which the theory of Ch. 3 can be used to obtain simple and satisfactory procedures for testing problems with a polyhedral-cone-shaped alternative. While dealing with the main problem \( \left( {{H_0},{{\tilde H}_1}} \right) \) with r>2, in which the alternative is determined by the pointed polyhedral cone K, one may proceed as follows. First the circular cone C = C(a, w) is specified as a substitute for K, next a particular test is selected for the modified problem \( \left( {{H_0},{{\tilde H}_1}} \right) \) of testing against C\(0 r), and finally this test is performed as a solution to the original problem (H0 , H1). Assuming that the choice of test for (H0 , \( {\tilde H_1} \)) is made in advance, the gist is to choose the axis a and the axial angle w of the substitute C for K, cf. (3.0.1). The special case r=2, where K itself is a circular cone, can be considered a benchmark for the comparison of various approaches to the main problem.


Multinomial Distribution Polyhedral Cone Linear Test Circular Cone Axial Angle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Johan C. Akkerboom
    • 1
  1. 1.Department of Statistical MethodsCentral Bureau of StatisticsHeerlenThe Netherlands

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