Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 03. For...
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Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 € 03. For simplicity, denote X₁ = (X₁1,..., Xik) and Xio = 1 - (Xi1 + … + Xik) for each i. Define the statistics 12 S; (X1:n) = Xij, i=1 j= 0, 1, 2,..., k. 2. Prove that T(X1:n) = (S1(X1:n), S2(X1:n)) is a sufficient statistic (SS) for by using (a) (15%) the definition of sufficiency; (b) (10%) Neyman-Fisher factorization theorem; and (c) (15%) the properties of exponential family. Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 € 03. For simplicity, denote X₁ = (X₁1,..., Xik) and Xio = 1 - (Xi1 + … + Xik) for each i. Define the statistics 12 S; (X1:n) = Xij, i=1 j= 0, 1, 2,..., k. 2. Prove that T(X1:n) = (S1(X1:n), S2(X1:n)) is a sufficient statistic (SS) for by using (a) (15%) the definition of sufficiency; (b) (10%) Neyman-Fisher factorization theorem; and (c) (15%) the properties of exponential family.
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a Let TX1n S1X1n S2X1n be the proposed statistic We want to show that for any the conditi... View the full answer
Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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