6.5.6. Suppose a sufficient statistic exists for the parameter θ. Use Theorem 5.6.1 to show that the critical region of a likelihood ratio test will depend on the sufficient statistic.

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Mathematics

Judith Dominguez

15 June, 18:14

6.5.6. Suppose a sufficient statistic exists for the parameter θ. Use Theorem 5.6.1 to show that the critical region of a likelihood ratio test will depend on the sufficient statistic.

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Huynh · Answer 1

Firstly, the defined parameters are X, Q, P, g, h, b

Let X1 = Q1, ... Xn, = Qn be a random sample of size n from the discrete Px

Step-by-step explanation:

Let X1 = Q1, ... Xn, = Qn be a random sample of size n from the discrete Px (k; θ) The statistic θ = h (X1, ..., Xn) is sufficient for if and only if there are functions g[h (Q1 ..., Qn.); θ]and b (Q1 ... Qn) such that L (θ) = g (h (Q1 ..., Qn); ) b (Qi ..., Qn) where the function b (Qi ... Qn) does not associate the parameter. A case holds in the continuous case.