Class Notes in Statistics and Econometrics Part 22 pdf
Class Notes in Statistics and Econometrics Part 22 pdf
... situations in which one would want to obtain a F -confidence region in order to get information about many different linear combinations of the parameters at the same time? For instance, one e xamines ... looks at only c ertain kinds of linear combinations, for instance, at all contrasts, i.e., linear combinations whose coefficients sum to zero. This is a very thorough way to ascertain that a...
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Class Notes in Statistics and Econometrics Part 1 pdf
... 1 Preface These are class notes from several different graduate econometrics and statistics classes. In the Spring 2000 they were used for Statistics 6869, syllabus on p. ??, and in the Fall 2000 for ... in B ∩ C, therefore it is also in the righthand side. If ω /∈ A and it is in the righthand side, then it must be both in B and in C, therefore i t is in the l...
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Class Notes in Statistics and Econometrics Part 3 pdf
... counter. They are hiding in the back, and whenever a customer steps up to the counter and rings the bell, they toss a coin. If the coin shows head, Herbert serves 152 5. SPECIFIC RANDOM VARIABLES will ... Pr[y=m and x=n]? Use a trick: express this intersection as the intersection of independent events. For this define z as the number of events in the interval (t, 1]. Then {y=m and...
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Class Notes in Statistics and Econometrics Part 19 pdf
... discussed in James and Stein [JS61], extending the work of Stein [Ste56]. Stein himself did not introduce the estimator as an “empirical Bayes” estimator, and it is not certain that this is indeed ... exercise? Stein rule estimators have not been used very much, they are not equivariant and the shrinkage seems arbitrary. Discussing them here brings out two things : the formulas for ra...
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Class Notes in Statistics and Econometrics Part 27 pdf
... Ξ) with X and v independent (and again for simplicity all variables having zero mean), which gives the same joint distribution of X and y as the above specification. Com- pute γ, V [x i ], and var[y i ] ... u and v have zero expected value and are independent of each other and of x ∗ . You have lots of data available, and for the sake of the argument we assume that the joint dis...
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Class Notes in Statistics and Econometrics Part 2 pptx
... intersection of a declining set sequence. And a converging sequence of nonnegative ε i which is not declining has a declining subsequence. A cumulative distribution function need not be continuous ... I.e., all the randomness is shunted off into the process of selecting an element of U . Instead of being an indeterminate function, it is defined as a determinate function of the random ω. It is...
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Class Notes in Statistics and Econometrics Part 4 pps
... 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 ... VARIANCE 221 Answer. Go back to throwing a coin twice independently and define A = {HH, HT }; B = {T H, HH}, and C = {HH, T T }, and x 1 = I A , x 2 = I B , and y = I C . They are...
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Class Notes in Statistics and Econometrics Part 5 pps
... 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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Class Notes in Statistics and Econometrics Part 6 pot
... chapter 3] According to Friedman’s permanent income hypothesis, drawing at random families in a given country and asking them about their income y and consumption c can be modeled as the independent ... point Therefore z 3 is a linear combination of y 1 and y 3 only. Compute its coefficients. • d. 1 point How does the joint distribution of z 1 , z 2 , and z 3 differ from that of y 1 ,...
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Class Notes in Statistics and Econometrics Part 7 ppt
... “indicator function” for nonnegative values, satisfying q(y) = 1 if y ≥ 0 and 0 otherwise. We will be working with the random variable which one obtains by inserting the j th observation y j into ... α 2 .) 370 13. ESTIMATION PRINCIPLES between the left and right hand side in (13.4.2) is called the Kullback-Leibler dis- crepancy between the random variables y and x (where x is a rando...
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