Supplement To: Permutation P -value Approximation via Generalized Stolarsky Invariance
نویسندگان
چکیده
Outline. This is an online supplement to the article “Permutation pvalue approximation via generalized Stolarsky invariance”. The section numbers pick up where the main article left off. Section 11 contains all but the shortest proofs of results in the main document. Section 12 investigates the effect of unbalanced sample sizes on the moments of the reference disributions. Section 13 analyzes the computational cost of computing p̂2 and its reference variance. Section 14 describes how to get the data we used.
منابع مشابه
Permutation p-value approximation via generalized Stolarsky invariance
Abstract: When it is necessary to approximate a small permutation pvalue p, then simulation is very costly. For linear statistics, a Gaussian approximation p̂1 reduces to the volume of a spherical cap. Using Stolarsky’s (1973) invariance principle from discrepancy theory, we get a formula for the mean of (p̂1− p)2 over all spherical caps. From a theorem of Brauchart and Dick (2013) we get such a ...
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