Abstract
Most large sample results for likelihood-based methods are related to asymptotic normality of the maximum likelihood estimator b MLE under standard regularity conditions. In this chapter we discuss these results. If consistency of b MLE is assumed, then the proof of asymptotic normality of b MLE is straightforward. Thus we start with consistency and then give theorems for asymptotic normality of b MLE and for the asymptotic chi-squared convergence of the likelihood-based tests TW,TS, and TLR. Recall that Strong consistency of b MLE means b MLE converges with probability one to the true value, and weak consistency of b MLE refers to b MLE converging in probability to the true value..
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Boos, D.D., Stefanski, L.A. (2013). Large Sample Results for Likelihood-Based Methods. In: Essential Statistical Inference. Springer Texts in Statistics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4818-1_6
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