Most Powerful Permutation Invariant Tests
      for Relatedness Hypotheses Using Genotypic Data

                   Anthony Almudevar

     Department of Mathematics and Computing Science
           Saint Mary's University 
       Halifax, N. S., Canada, B3H 3C3,
      e-mail: anthony.almudevar@stmarys.ca

Abstract

A class of tests for permutation invariant relatedness hypotheses
using genotypic data is proposed, which are proven to
be of maximum power among permutation invariant tests.
These tests lead naturally to "locally most powerful tests",
in the sense that power is maximized for alternatives
statistically close to a null hypothesis of unrelatedness.
Although the resulting statistic is a U-statistic, normal
approximation theory is found to be inapplicable, due to
high skewness. As an alternative it is found that a conditional procedure
based on the most powerful test statistic can calculate accurate
significance levels without much loss in power. Examples are given
in which this type of test proves to be more powerful than a number
of alternatives considered in the literature, including Queller and
Goodknight's (1989) estimate of genetic relatedness, the average number
of shared alleles (Blouin, 1996) and the number of feasible sibling
triples (Almudevar and Field, 1999).

Key words: most powerful invariant test, genotypic data,
relatedness inference, conditional tests