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 ... 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

... 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 jointly normal random ... independent.  Problem 136. If the vector random variables x and y have the property that x i is independent of every y j for all i and j, does that make x and y independent random ve...

Ngày tải lên: 04/07/2014, 15:20

... 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...

Ngày tải lên: 04/07/2014, 15:20

... 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...

Ngày tải lên: 04/07/2014, 15:20

... 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...

Ngày tải lên: 04/07/2014, 15:20

... 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...

Ngày tải lên: 04/07/2014, 15:20

... 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...

Ngày tải lên: 04/07/2014, 15:20

... 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

... 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...

Ngày tải lên: 04/07/2014, 15:20

... 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...

Ngày tải lên: 04/07/2014, 15:20