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

Matthieu R Bloch Tuesday, March 24, 2020

TUTORIAL TUTORIAL

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MLE FOR UNIFORM DISTRIBUTIONS MLE FOR UNIFORM DISTRIBUTIONS

Assume that you have access to i.i.d. realization of

• f a uniformly distributed random variable

. Show that the maximum likelihood estimator for the parameters when is uniform on are Show that the maximum likelihood estimator for the parameters when is uniform on is

{xi}N

i=1

X a < b X [a; b] = = . a ^ min

i

xi b ^ max

i

xi a > 0 X [−a; a] = | |. a ^ max

i

xi

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3

4

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MLE FOR UNIFORM DISTRIBUTIONS MLE FOR UNIFORM DISTRIBUTIONS

Now assume that is uniform on with . Show that the estimator is well defined, in the sense that . Show that the estimator is well defined, in the sense that . Which of

• r

is the maximum likelihood estimator?

X [a; 2a] a > 0 = a ^1 mini xi ∀i ≤ ≤ 2 a ^1 xi a ^1 = a ^2

maxi xi 2

∀i ≤ ≤ 2 a ^2 xi a ^2 a ^1 a2 ^

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7

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