[試題] 98上張勝凱計量方法入門期末考

看板NTU-Exam作者reluctant (生命就是燃燒)時間16年前 (2009/09/12 22:00)推噓7(7推 0噓 4→)

留言11則, 5人參與討論串1/1

課程名稱︰計量方法入門課程性質︰必修課程教師︰張勝凱開課學院：社會科學院開課系所︰經濟研究所考試日期（年月日）︰98年9月11日考試時限（分鐘）：100 是否需發放獎勵金：是（如未明確表示，則不予發放）試題 : Problem 1. True of False (25 points (5,5,5,5,5)) 1. If yi = xi'β + εi, xi is an element of R and E(εi|xi) = 0, then εi is independent of xi. 2. If yi = xi'β + εi, xi is an element of R and E(εi|xi) = 0, then E(xi^2εi) = 0. 3. If yi = xi'β + εi, xi is an element of R and E(xiεi) = 0, then E(xi^2εi) = 0. 4. If Y is uncorrelated with E(Y|X), then Y is uncorrelated with X. 5. If Y is mean independence of X, then Y^2 is mean independence of X. Problem 2.(25 points (5, 10, 10)) Let θcap = (θ1cap, θ2cap)' be a N square-root- asymptotically normal estimator for θ = (θ1, θ2)'. Let γcap = 2θ1capθ2cap be an estimator of γ = 2θ1θ2. 1. Is γcap a consistent estimator of γ? Explain. 2. Find Avar(γcap) in terms of θ and Avar(θcap). 3. If, for a sample of data, θcap = (1,2)' and Avar(θcap) is estimated as [1 -0.5 ] [-0.5 2 ] find the asymptotic standard error of γcap. Problem 3.(25 points (5,10,10)) Let the joint pdf by f(x,y) = 6xy^2 , 0 < x < 1, 0 < y < 1. = 0 , elsewhere (1) Verify f(x,y) is a legitimate joint pdf function. (2) Find E(Y|X). Is Y mean independent of X ? (3) Find BLP of Y given X. Is Y uncorrelated with X ? Problem 4.(25 points (15,10)) (a) Let Xi, i = 1,2,.... be an independent Berboulli(p) random variables and let Yn = ΣXi / n. Then, find the asymptotic distribution of Yn/(1-Yn). (b) Let X1, ..., Xn be a random sample from a population with meanμ and varianceσ^2. Find E((Xnbar - μ)n^0.5/2σ) and Var((Xnbar - μ)n^0.5/2σ). -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.193.251.73 ※ 編輯: reluctant 來自: 123.193.251.73 (09/12 22:02)

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gavin79115

09/12 22:23, , 1^F

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Jackliu2619

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Jackliu2619

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