Linear Models II
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چکیده
Theorem 1. Assume that β ∈ R and that X is a n × k matrix of rank k < n. Let Y1, . . . , Yn are independent normally distributed random variables with mean vector μ = Xβ. Then, the likelihood ratio test of the hypothesis H0 : Aβ = 0 versus H1 : Aβ 6= 0. where A is a q × k matrix has critical region C = {y;F (y) ≥ F0}. F is given by F (y) = ∑n i=1(yi − ̂̂ μi) −∑ni=1(yi − μ̂i) ∑n i=1(yi − μ̂i) n− k q . (1)
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