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7. Lecture 8. Composite hypotheses Lecture 8. Composite hypotheses ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-08-composite-hypotheses.pdf20 Feb 2017: The ’generalised likelihood ratio test’. The next theorem allows us to use likelihood ratio tests even when we cannotfind the exact relevant null distribution. ... Generalised likelihood ratio tests. The 'generalised likelihood ratio test'. -
1 Statistics 1B Interludes 10. Multiple testing Testing many ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/interlude-10-multiple-testing.pdf28 Feb 2017: Suppose test n H0i with independent test statistics. Prob(at least one will reject an H0i| H0i true) = 1 – Prob(reject none). = ... So a simple method is to multiply the observed significance level by the number of tests. -
14. Lecture 15. Hypothesis testing in the linear model ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-15-linear-hypotheses.pdf6 Mar 2017: Generalised likelihood ratio test. The generalised likelihood ratio test of H0 against H1 is. ... Hypothesis testing in the linear model 15.5. Null distribution of test statistic. -
6. Lecture 7. Simple Hypotheses Lecture 7. Simple Hypotheses ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-07-simple-hypotheses-4.pdf6 Feb 2017: It says that the most powerful test (ie the one with the smallest Type II errorprobability), among tests with size smaller than or equal to α, is the size αlikelihood ratio ... This is called a z-test. Lecture 7. Simple Hypotheses 9 (1–1). -
7. Lecture 8. Composite hypotheses Lecture 8. Composite hypotheses ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-08-composite-hypotheses-4.pdf20 Feb 2017: W (θ) W(θ) for all θ Θ1. UMP tests may not exist. ... The ’generalised likelihood ratio test’. The next theorem allows us to use likelihood ratio tests even when we cannotfind the exact relevant null distribution. -
14. Lecture 15. Hypothesis testing in the linear model ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-15-linear-hypotheses-4.pdf6 Mar 2017: Generalised likelihood ratio test. The generalised likelihood ratio test of H0 against H1 is. ... Hypothesis testing in the linear model 15.5. Null distribution of test statistic. -
15. Lecture 16. Linear model examples, and ’rules of ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-16-linear-examples.pdf6 Mar 2017: Thus D N(µX µY , φ2. n ), and we test H0 : µX µY = 0 by the t statistic. ... 16. Linear model examples 16.2. Paired observations. In R code:. > t.test(x,y,paired=T). -
Mathematical Tripos: Part IB DJS/Lent 2017 Statistics: Example Sheet…
www.statslab.cam.ac.uk/Dept/People/djsteaching/ex-S1B-17-1.pdf17 Jan 2017: Comments and corrections to david@statslab.cam.ac.uk. 1. Ask your supervisor to test you on the sheet of common distributions handed out inlectures. -
15. Lecture 16. Linear model examples, and ’rules of ...
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-16-linear-examples-4.pdf6 Mar 2017: A size α test is to reject H0 if |t| > tnm2(α/2). ... 16. Linear model examples 16.2. Paired observations. In R code:. > t.test(x,y,paired=T). -
10. Lecture 11. Multivariate Normal theory Lecture 11. Multivariate…
www.statslab.cam.ac.uk/Dept/People/djsteaching/S1B-17-11-MVN.pdf7 Mar 2017: sheet 3 for use of t distributions in hypothesis tests.Lecture 11.
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