[試題] 98上 張勝凱 計量方法入門 期末考

[reluctant (生命就是燃燒)]

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).


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◆ From: 123.193.251.73
※ 編輯: reluctant       來自: 123.193.251.73       (09/12 22:02)
推 gavin79115  :98上不是還沒開始嗎@@XD
推 Jackliu2619 :原po批幣缺很大喔 科科 這科的開課方式考古題應該僅
→ Jackliu2619 :供參考而已吧 XD
推 abacada     :期前考?
→ TINTINH     :這個我也不知道是不是該收在經濟系 請板主指示 感謝!
推 youngsam    :經濟所碩一必修課  於暑假上課
→ youngsam    :不過每年授課老師有可能不同
→ youngsam    :授課內容也由授課老師決定
推 abacada     :看樣子是98上沒錯 只是暑假就開課這樣
推 abacada     :大概像一些科法所那樣吧  經研所的課  麻煩小板主囉~