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# Consider, sampling from a multivariate normal distribution with mean vector = (1 ISBN: 9780130661890 386

## Solution for problem 11 Chapter 17

Econometric Analysis | 5th Edition

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Problem 11

Consider, sampling from a multivariate normal distribution with mean vector = (1, 2,...,M) and covariance matrix 2I. The log-likelihood function is ln L = nM 2 ln(2) nM 2 ln 2 1 22 n i=1 (yi ) (yi ). Show that the maximum likelihood estimates of the parameters are 2 ML = n i=1 M m=1 (yim ym)2 nM = 1 M M m=1 1 n n i=1 (yim ym) 2 = 1 M M m=1 2 m. Derive the second derivatives matrix and show that the asymptotic covariance matrix for the maximum likelihood estimators is E 2 ln L 1 = 2I/n 0 0 24/(nM) . Suppose that we wished to test the hypothesis that the means of the M distributions were all equal to a particular value 0. Show that the Wald statistic would be W = (y 0 i) 2 n I 1 (y 0 i), = ! n s2 " (y 0 i) (y 0 i), where y is the vector of sample means.

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Week 10 Notes for FIN 305 10/24 Standard Deviation ­Equal to the amount of risk ­Probability vs Range ­68% = +/­ 1 STD ­95% = +/­ 2 STD ­99% = +/­ 3 STD *Usually easier to draw without the bell curve *The higher STD, the higher the risk CV = Coefficient Value ­Decision rule regarding this: ­Want...

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##### ISBN: 9780130661890

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