For testing H 0 Iuml j Iuml j0 j 1, ,c, using sample multinomial proportions Iuml Igrave j , the likelihood ratio statistic (1 17) is Show that G 2 yen 0, with equality if and only if Iuml Igrave j Iuml j0 for all j (Apply Jensens inequality to E(2n log X), where X equals Iuml j0 Iuml Igrave j with...

Let X be a random variable that equals j0 j wi ...

For testing H 0 : Ï j = Ï j0 j = 1,. . . ,c, using

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For testing H₀: Ï€_j= Ï€_j0j = 1,. . . ,c, using sample multinomial proportions {Ï€Ì‚_j}, the likelihood-ratio statistic (1.17) is

Show that G² ‰¥ 0, with equality if and only if Ï€Ì‚_j= Ï€_j0for all j. (Apply Jensen€™s inequality to E(€“2n log X), where X equals Ï€_j0/Ï€Ì‚_jwith probability Ï€Ì‚_j.)

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Categorical Data Analysis

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Authors: Alan Agresti

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For testing H 0 : Ï j = Ï j0 j = 1,. . . ,c, using

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G² = -2n L îî; log(7;0/ î;). îr, log(™j0/ îr;,

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Categorical Data Analysis

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