TUTORIAL TUTORIAL Matthieu R Bloch Tuesday, March 24, 2020 1 MLE - PowerPoint PPT Presentation

TUTORIAL TUTORIAL Matthieu R Bloch Tuesday, March 24, 2020 1

MLE FOR UNIFORM DISTRIBUTIONS MLE FOR UNIFORM DISTRIBUTIONS Assume that you have access to i.i.d. realization of of a uniformly distributed random variable { x i } N i =1 . X Show that the maximum likelihood estimator for the parameters when is uniform on are a < b X [ a ; b ] ^ a ^ = min x i b = max x i . i i Show that the maximum likelihood estimator for the parameters when is uniform on is a > 0 X [− a ; a ] a = max | x i |. ^ i 2

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MLE FOR UNIFORM DISTRIBUTIONS MLE FOR UNIFORM DISTRIBUTIONS Now assume that is uniform on with . X [ a ; 2 a ] a > 0 Show that the estimator is well defined, in the sense that . a = min i x i ∀ i a ≤ x i ≤ 2 a ^ 1 ^ 1 ^ 1 Show that the estimator is well defined, in the sense that . max i x i a ^ 2 = ∀ i a ^ 2 ≤ x i ≤ 2 a ^ 2 2 Which of or is the maximum likelihood estimator? a a 2 ^ 1 ^ 6

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