Genotypes AA, Aa, and aa occur with probabilities [ 2 , 2(1 ), (1 )
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Genotypes AA, Aa, and aa occur with probabilities [θ2, 2θ(1 – θ), (1 – θ)2]. A multinomial sample of size n has frequencies (n1, n2, n3) of these three genotypes.
a. Form the log likelihood. Show that θ̂ = (2n1 + n2)/(2n1 + 2n2 + 2n3).
b. Show that –∂2L(θ)/∂θ2 = [(2n1 + n2)/θ2] + [(n2 + 2n3)/(1 – θ)2] and that its expectation is 2n/θ(1 – θ). Use this to obtain an asymptotic standard error of θ̂.
c. Explain how to test whether the probabilities truly have this pattern.
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a The kernel of the log likelihood is L n 1 log 2 n 2 log 21 n 3 log 1 2 Take L 2n 1 n ...View the full answer
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