Class Notes in Statistics and Econometrics Part 18 pps

... do something which he do e s not quite understand is in the above eliciation of prior information. It often happens that prior information gained in this way is self- contradictory, and the researcher ... and variance alone. Problem 395. 4 points Show that, if y is normally distributed, s 2 and ˆ β are independent. Answer. We showed in question 300 that ˆ β and ˆε are uncorrelat...

Ngày tải lên: 04/07/2014, 15:20

... 227 Problem 140. 2 points Given two independent random variables x and y with density functions f x (x) and g y (y). Write down their joint, marginal, and conditional densities. Answer. Joint density: ... argument inside. 220 8. VECTOR RANDOM VARIABLES 1), and if cov[x, y] = 0, then x and y are independent. (I.e., in this respect indicator variables have similar properties as join...

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... the inner integral becomes − 1 2π e −t   ∞ 0 = 1 2π ; therefore the whole integral is 1. Therefore the product of the integrals of the marginal densities is 1, and since each such marginal integral ... First we will introduce the multivariate standard normal, which one obtains by applying only operations (1) and (2), i.e., it is a vector composed of independent univariate standard norma...

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... 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 ... statistical or sampling prop e rties. We are assuming right now the specification given in (18. 1.3), in which X is an arbitrary matrix of full column rank, and we are not assuming tha...

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... linear in P y are also linear in y and vice versa, ˆ β is also the BLUE in the original GLS model. Problem 319. 2 points Show that (26.0.3) ˆ β −β = (X  Ψ −1 X) −1 X  Ψ −1 ε ε ε and derive from this ... than those familiar from linear estimators. The problem at hand can be reduced to a minimum trace problem as defined in Rao [Rao73, pp. 65–66], and part of the following proof...

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... 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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... within-group or between-group phenomena or both.: • negative relationship of protein % and oil % (both within • and ◦); • p osit ive relationship of oil % and seed size (both within • and ◦ and ... of seed size and height; • p osit ive relationship of height and lodging (within ◦ and between groups); • negative relationship of oil % and lodging (between groups and possibly...

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... 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 known, and their joint ... minimize the relative increase in the Maha- lanobis distance (instead of selecting its minimax value) because all parameters of the underlying distribution were known. The simplest si...

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... u t is independent of ε s−1 . Since s < t, therefore in particular s = t, u t is also independent of u s . Therefore u t is independent of any function of ε s−1 and u s , in particular, it is independent ... process independent of the pre-sample disturbance ε 0 , and α 0 > 0 and 0 < α 1 < 1 are two constants. • a. 2 points Show that u t is independent of all ε s with 0...

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... 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 ... causality should be included in statistics textbooks. Innovation accounting or impulse response functions: make a moving average representation, and then you can pick the timepath of...

Ngày tải lên: 04/07/2014, 15:20