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29 Apr 2014: and on the other, the variances andcovariances of asset returns, which could all be estimated very easily from market data7, therebyproviding a test of the CAPM analysis. ... 1.4 Equilibrium pricing. We cannot pass by this place without pausing to see

13 Oct 2014: Our methods to exclude candidate curves include 2-Selmer, 4-Selmer, and 8-Selmer tests, the use of the Guinand-Weil explicit formula, and even 3-descent in a couple of

12 Feb 2014: Isthe test uniformly most powerful for testing H0 : θ = θ0 against H1 : θ > θ0? ... By first deriving the MLEs under each hypothesis, showthat the likelihood ratio and Pearson’s chi-squared tests are identical to those for theindependence test.

28 Jan 2014: 10. This question is about understanding what can happen to the F-test when the expectedvalue of the response is not necessarily linear in β. ... Suppose we try to test the hypothesis H0 : β1 = 0 against the alternative H1 : β1 6= 0 byrejecting the

28 Feb 2014: SXX/(n1)}1/2. Determine the distribution of T under H0, and hence. determine the size α likelihood ratio test. ... size α likelihood ratio test of equality of means rejects H0 if.

18 Feb 2014: ε̂i = (1 pi)(Yi xTi β̂(i)). How can we construct a hypothesis test based on η̃i to test whether the ith obser-. ... Fit a linear model to the log-transformed data and then applyyour hypothesis test to check whether the observation corresponding to

24 Jan 2014: Comments and corrections to s.pitts@statslab.cam.ac.uk. 1. Ask your supervisor to test you on the sheet of common distributions handed out inlectures.

13 Oct 2014: tests, the use of the Guinand-Weil explicit formula, and even 3-descent in a couple. ... The 50% percentile reached Σ5 37.7, with 332 curvessurviving the 4-descent test.

17 Mar 2014: ββT. Find β̂3 and var (β̂3), and show how you would test H0 : β3 = 0, when σ2 is. ... 2, henceβ̂3 has variance σ. 2/Σ(P2(xi))2, and is normally distributed. We can test H0 : β3 = 0 , by referringβ̂3/.

3 Oct 2014: We’ll comment on this again later in the case of algebraic curves, where a more useful test.