Theory of Nonparametric Tests by Thorsten Dickhaus

Author:Thorsten Dickhaus
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

with denoting the expectation with respect to and scores .

Remark 4.21

(a)The test statistic

(4.8)

is called a linear rank statistic.

(b)The homogeneity hypothesis H 0 from (4.3) leads under conditioning on R(Y ) to a simple null hypothesis on , namely, the discrete uniform distribution on , see part (b) of Lemma 4.13. Therefore, the critical value c(α) for the rank test φ = φ(R(Y )), given by

(4.9)

can be computed by traversing all possible permutations and thereby determining the discrete permutation distribution of T(Y ) under H 0. The test φ from (4.9) is a locally best rank test at level α for the test problem {𝜗 = 0} versus {𝜗 > 0} in the chosen auxiliary parametric model , cf. Example 4.10. For large n, we can approximate c(α) by traversing only B < n! randomly chosen permutations .

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.