1.If data show as follows:
y x omega Σ
3 1 6 3 2 3 2
2 1 3 2 1 6
1 1 1 3 6 1
,then what is the ols b( 1,1)=?, varcov of b(1,1)=?
and the gls b(1,1)= ?
2.(1) If LoglikR=100,LoglikU=110, then LR test statisticsχ2 =?
ans: 20
(2) c(θ)=q is [ 1 2; 3 4] [θ1 ;θ2] = [1; 2]
If we estimate the mle and obtain that 1=3, 2=3,
and Var(c( -q))=[ 2 1; 1 3], then find the Wald test?
3.If n=20, k=3, ESSr=200 , ESS1=50 , ESS2=30
Chow test=?
4.If the likelihood function of the normal distribution is
–n/2ln(2p)-n/2ln(s2)-1/2Σ((x-m)/s)^2 , and the sample data is
xi=(3 6 9) (ie n=3), then what is the mle m and s
5.If we want to maximize the loglikelihood function by BHHH method and set
the initial value at m=3,(s is known and = 1). what will be next itiration
of m
以上的m = mean(音：mu） s=(sigma標準差)
在此謝謝各位大大！！
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