iid Let X1,..., Xn Beta(0, 1) with pdf f(x; 0) = 0xº-1 for 0 0. a) Show that the maximum likelihood estimator of 0 is n 1 ÔM LE log(x;) -- 500, suppose that the maximum likelihood estimate of 0 takes value 0 = 1.2. Use the parametric bootstrap method to obtain a 95% revised bootstrap percentile confidence interval of the maximum likelihood estimate. b) Given a sample of size n = %3D

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Let X1,..., Xn Beta(0,1) with pdf f(x;0) = 0x®=1_for 0 < x<1, and 0 > 0.
iid
a)
Show that the maximum likelihood estimator of 0 is
ÔMLE
Elog(x;)
i=1
500, suppose that the maximum likelihood estimate of 0
takes value 0 = 1.2. Use the parametric bootstrap method to obtain a 95% revised bootstrap
percentile confidence interval of the maximum likelihood estimate.
b)
Given a sample of size n =
Transcribed Image Text:Let X1,..., Xn Beta(0,1) with pdf f(x;0) = 0x®=1_for 0 < x<1, and 0 > 0. iid a) Show that the maximum likelihood estimator of 0 is ÔMLE Elog(x;) i=1 500, suppose that the maximum likelihood estimate of 0 takes value 0 = 1.2. Use the parametric bootstrap method to obtain a 95% revised bootstrap percentile confidence interval of the maximum likelihood estimate. b) Given a sample of size n =
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