2018/06/22 by Mitchell, Jonathan D., Allman, Elizabeth S., Rhodes, John A. · 1 citation
#62E17 #92D15 #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1806.08458
The likelihood ratio statistic, with its asymptotic χ2 distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be χ2, as highlighted by recent work of Drton. Indeed, poor behavior of a χ2 for testing near singularities and boundaries is apparent in simulations, and can lead to conservative or anti-conservative tests. Here we develop a new distribution designed for use in hypothesis testing near singularities and boundaries, which asymptotically agrees with that of the likelihood ratio statistic. For two example trinomial models, arising in the context of inference of evolutionary trees, we show the new distributions outperform a χ2.