This document discusses the maximum likelihood estimator, its calculation, and properties, including bias and convergence.
Contents
Exercise 1
Exercise 2
Exercise 3
Exercise 1
Exercise 2
Exercise 3
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[...] A biased estimator can converge while an unbiased estimator may not converge necessarily. Exercice 2 One calculates first the likelihood: , then we take its logarithm: The maximum is reached when the derivative is zero: from where: et enfin . This is therefore the maximum likelihood estimator of . Exercise 3 We first calculate the likelihood: , then we take its logarithm: The maximum is reached when the derivative is zero: d'où : So it is the maximum likelihood estimator of . [...]
