Class Notes in Statistics and Econometrics Part 5 pps
Class Notes in Statistics and Econometrics Part 5 pps
... Ψ 1 = 0.62 −0 .56 −0 .56 1.04 , Ψ 2 = 1. 85 1.67 1.67 3.12 , Ψ 3 = 0.62 0 .56 0 .56 1.04 , Ψ 4 = 1. 85 −1.67 1.67 3.12 , Ψ 5 = 3.12 −1.67 −1.67 1. 85 , Ψ 6 = 1.04 0 .56 0 .56 0.62 , ... vertical band between 0.4 and 2.6 and the horizontal band between 3 and -1 roughly have the same probability as the ellipse, namely 95% . Since a univariate Normal has 95%...
Ngày tải lên: 04/07/2014, 15:20
Class Notes in Statistics and Econometrics Part 4 pps
... cases: (8.0.9) Second Flip H T sum First H . 25 . 25 .50 Flip T . 25 . 25 .50 sum .50 .50 1.00 Second Flip H T sum First H .50 .00 .50 Flip T .00 .50 .50 sum .50 .50 1.00 The most important case is that ... = 30 and var[x] = 180 · (5/ 36) = 25. Therefore define y ∼ N(30, 25) . The CLT says that Pr[x≥ 25] ≈ Pr[y≥ 25] . Now y≥ 25 ⇐⇒ y − 30≥ − 5 ⇐⇒ y − 30≤ + 5 ⇐⇒ (y −30) /5 1. Bu...
Ngày tải lên: 04/07/2014, 15:20
Class Notes in Statistics and Econometrics Part 12 ppsx
... lefthand side; it is amazing and surprising that it is exactly the population equivalent of the F -test for testing α = 0 in the regression with intercept. It can be estimated by replacing α 2 with ... the following: Theorem 24.2.2. ˆ β is a linear minimax est imator of the parameter vector β in the following sense: for every nonrandom coefficient vector t, t ˆ β is the linear 640 24. S...
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Class Notes in Statistics and Econometrics Part 13 pps
... defined in Rao [Rao73, pp. 65 66], and part of the following proof draws on a private communication of C. R. Rao regarding consistency of equation (1f.3.4) in [Rao73, p. 65] . Proof of theorem 25. 2.3: ... true β. Barnard’s s uggestion has not found entrance into the textbooks and indeed, since linear estimators in model ( 25. 0.12) are unbiased if and only if they have bounded MS...
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Class Notes in Statistics and Econometrics Part 14 ppsx
... best linear bounded MSE predictor of z based on y, µ, and ν. • a. Give special cases of this specification in which µ and ν are constant and y and z random, and one in which µ and ν and y are random ... are random and z is constant, and one in which µ and ν are random and y and z are constant. 27.1. MINIMUM MEAN SQUARED ERROR, UNBIASEDNESS NOT REQUIRED 713 informa...
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Class Notes in Statistics and Econometrics Part 17 pps
... searches for an interesting and informative projec- tion of the data by maximizing a criterion function. A logical candidate would for instance be the variance ratio as defined in (8.6.7), but ... size (both within • and ◦ and also between these groups); • negative relationship, between groups, of seed size and height; • p osit ive relationship of height and lodging (within ◦ and...
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Class Notes in Statistics and Econometrics Part 18 pps
... between 0. 75 and 0. 95, and there is a 50 -50 chance that it lies above or below 0. 85. The least squares estimate of the MPC is 0.9, with a reasonable confidence interval. There is no multicollinearity involved, ... vector, since we follow the “column vector convention.” The (marginal) 855 35. LEAST SQUARES AS THE NORMAL MAXIMUM LIKELIHOOD ESTIMATE 857 If we replace β in the log...
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Class Notes in Statistics and Econometrics Part 20 pps
... even start to prove it. There is a proof in [Kme86, pp. 749– 757 ], and one in [Mal80, pp. 53 5 53 9]. Problem 411. Since least squares with random regressors is appropriate when- ever the disturbances ... Scenario: Minimizing relative increase in Mahalanobis distance i f distribution is known We start with a situation where the e xpec ted values of the random vectors y and z are k...
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Class Notes in Statistics and Econometrics Part 29 ppsx
... points for 0.0 05% F (5, 15; 0.0 05) = 5. 37 (which g ives a two-sided 1% significance level), for 1% it is F (5. 15; 0.01) = 4 .56 (which gives a two-sided 2% significance level), for 2 .5% F (5, 15; 0.0 25) = ... 2 .5% point one can also use the Splus-command qf(1 -5/ 200 ,5, 15) . One can also get the lower significance points simply by the command qf (5/ 200 ,5, 15) . The test is the...
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Class Notes in Statistics and Econometrics Part 34 pps
... back, and you regress y on X with a constant term. (The under- lining does not denote taking out of the mean, but the taking out of the seasonal means and adding back of the overall mean.) In the ... draw causal inferences from his or her data, and the discussion of causality should be included in statistics textbooks. Innovation accounting or impulse response functions: make a mo...
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