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27 Apr 2023: By first deriving the MLEs under each hypothesis, show that the likelihood ratio andPearson’s chi-squared tests are identical to those for the independence test. ... Is the test uniformly most powerfulfor testing H0 : θ = θ0 against H1 : θ > θ0?

4 Jul 2023: 15:00-16:00 Natalie Packham - Berlin School of Economics and Law. Correlation scenarios and correlation stress testing slides.

28 Apr 2023: What arethe size and power of the test in terms of α and β? ... Is φkadmissible as a test of H0 against Hθ for every θ (0, 1)?

31 Oct 2023: From this limiting result: (i) derive a test for the hypothesis H0 : θ = θ0 vs. ... For all these models, derive explicit expressions for the likelihood ratio test statistic ofa simple hypothesis test of H0 : θ = θ0, θ0 Θ, vs.

27 Apr 2023: test to test the hypothesis H1 : σ2 > σ̃2 against the hypothesis H0 : σ. ... 2 = σ̃2. Does the F-test depend on whether µ, µ̃ are known?

18 Apr 2023: Outline. A short summary of Michael’s CV. Stochastic optimization, Financial Economics and Computations. ... Research path (3): Financial economics. There wouldn’t be a research area as applied stochastic optimization to economics and finance

28 Apr 2023: Explain why for large n thelikelihood-ratio test and the t-test are nearly the same. ... Howcould you use this to make a test of H0 against H1 : µ Θ1?

27 Apr 2023: From this limiting result: (i) derive a test for the hypothesis H0 : θ = θ0 vs. ... For all these models, derive explicit expressions for the likelihood ratio test statistic ofa simple hypothesis test of H0 : θ = θ0, θ0 Θ, vs.

28 Apr 2023: You do not need to derive the test.] What conclusion shouldbe reported to the doctor? ... What is the size of this test? Write down an expression forits power.

27 Apr 2023: 8H StatisticsDefine a simple hypothesis. Define the terms size and power for a test of one simple. ... Construct a best test of size 0.05 for the null hypothesis.