ECON 710 Final: ECON 710 UW Madison Final Exam 2009a

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31 Jan 2019
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1. (a) estimator: (b) percentile bootstrap: draw an observation (y(cid:3, repeat this n times, to obtain a sample fy(cid:3) ig; i = 1; :::; n, compute the estimator ^(cid:22)3 on this bootstrap sample. This is i ) randomly from the observed sample fyi; xig i ; x(cid:3) i ; x(cid:3) i ! (cid:0)1 nxi=1 (cid:3) i! i y(cid:3) x(cid:3) i x(cid:3)0 x(cid:3) (cid:3) ^(cid:12) i i = y(cid:3) i (cid:0) x(cid:3)0. ^(cid:22)(cid:3: repeat this b times, to obtain f^(cid:22)(cid:3, let ^q:05 and ^q:95 be the 5% and 95% empirical quantiles of ^(cid:22)(cid:3) [:05(b + 1)](cid:146)th and [:95(b + 1)](cid:146)th order statistics of ^(cid:22)(cid:3) 3b: the efron percentile con(cid:133)dence interval for (cid:22)3 is [^q:05; ^q:95] 2. (a) the estimated covariance matrix for ^(cid:12) 1; ^(cid:12) 2 is. ^(cid:26)s(^(cid:12) 1)s(^(cid:12) 2) s(^(cid:12) 2)2 (cid:21) (recall that the standard errors are the square roots of the diagaonal elements of the estimated covariance matrix).

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