Consider independent observations y_(1), dots, y_(n) from the model Y_(i)~ Poisson (mu). Using likelihood L(mu) and...

 

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Consider independent observations y_(1), dots, y_(n) from the model Y_(i)~ Poisson (mu). Using likelihood L(mu) and loglikelihood I(mu) as appropriate, compute the following items. Derive the maximum likelihood estimate hat(mu). Write the second derivative of log-likelihood I(mu). Give an expression of the approximated asymptotic standard error of hat(mu) by plugging in the estimate hat(mu). To this end, estimate the Fisher Information Matrix by hat(V)=- (del^(2))/(delmu^(2)) (mu)|_(mu= hat(mu)) and then s.e. (hat(mu))-sqrt( hat(V)^(-1)). Consider data 23, 14, 16, 22, 18, 22, 24, 30. Using your formul, compute and write numerical estimates hat(mu), s. e. (hat(mu)) and give a 95% confidence interval for mu using the normal approximation. Consider independent observations y_(1), dots, y_(n) from the model Y_(i)~ Poisson (mu). Using likelihood L(mu) and loglikelihood I(mu) as appropriate, compute the following items. Derive the maximum likelihood estimate hat(mu). Write the second derivative of log-likelihood I(mu). Give an expression of the approximated asymptotic standard error of hat(mu) by plugging in the estimate hat(mu). To this end, estimate the Fisher Information Matrix by hat(V)=- (del^(2))/(delmu^(2)) (mu)|_(mu= hat(mu)) and then s.e. (hat(mu))-sqrt( hat(V)^(-1)). Consider data 23, 14, 16, 22, 18, 22, 24, 30. Using your formul, compute and write numerical estimates hat(mu), s. e. (hat(mu)) and give a 95% confidence interval for mu using the normal approximation.