Asymptotic Distribution of the Maximum Likelihood Ratio Test for Gene Detection

摘要

This paper deals with the asymptotic distribution of the test process obtained by estimating the effect of a gene acting on a quantitative trait. Convergence is studied when the number of individuals and genetic markers goes to infinity. It is proved that this process converges in distribution to an Ornstein #x2013; Uhlenbeck diffusion process under the null hypothesis, and to the same Ornstein #x2013; Uhlenbeck process superimposed on a mean value function under local alternatives. To ensure this convergence, we derived the necessary relation between the number of individuals and the maximum distance between two consecutive markers.