Inferential Statisticshard
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Consider the likelihood ratio test for H0:θ=θ0H_0: \theta = \theta_0 versus H1:θ≠θ0H_1: \theta \neq \theta_0. If the log-likelihood function is ℓ(θ)\ell(\theta), the statistic λ=−2(ℓ(θ0)−ℓ(θ^))\lambda = -2(\ell(\theta_0) - \ell(\hat{\theta})) is used. Under the null hypothesis, what is the asymptotic distribution of λ\lambda as n→∞n \to \infty?