Likelihood Ratio Test of a Class of Mixture Model

In this paper, a class of mixture model g(x)=(1-ζ₁-ζ₂)f(x,θ₀')+ζ₁f(x,θ_i')+ζ₂f(x,θ₂'),is discussed, where 0≤ζ₁,ζ₂,ζ₁+ζ₂≤1, f is a probability density function, and θ_i'(i=0,1,2) is a m-dimensional constant vector. The limit distribution of likelihood ratio statistic of the model is given.