Unformatted text preview: , : , and : , 2 1 2 1 2 1 2 1 = Ω = = Ω Q.2. Give the ML estimators (formulas) for θ 1 ,θ 2 for Ω, and θ = θ 1 = θ 2 for Ω Q.3. Give the Likelihood Ratio Test Statistic (Formula) and Rejection Region for this test. Q.4. Give the Wald (Z) Test Statistic (Formula) and Rejection Region for this test (based on largesample normal approximation). Q.5. Generate 10000 random samples of size 20 from Exp( θ 1 ) and Exp( θ 2 ) and obtain the following quantities: ( 29 obs Y X Z S Y S X , ln 2 , , , , , , , ^ 2 ^ 1 ^ 2 2 λQ.6. Give histograms of your test statistics (for the Wald test, give a histogram of (Z obs ) 2 ≈ Chisquare (df=1)) Complete this for the following values for θ 1 ,θ 2 θ 1 θ 2 Pr{Reject H } – LR Test Pr{Reject H } – Wald Test 1000 1000 1100 1000 1200 1000...
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 Spring '10
 Winner
 Statistics, Statistical hypothesis testing, Statistical tests, Likelihoodratio test, Likelihood principle, Brand B

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