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Let X1, , X, be iid with population pdf given by h ( which integrates to 1 over the real line. Here, the location parameter u E (-0, 00) and the scale parameter ao Denote log(h(z)) by (z). Denote the first and second derivatives of th by t and 3, respectively. where h is a positive twice-differentiable function a. Show that the score vector equals -- - () h Hence, or otherwise, show that E(O(X)) = 0 and E(Xp(X)) =-1 where the expectation here and below is calculated under the assumption that u 0 and o 1. S Show that the Fisher information matrix due to a single X is given by -E(x(X)) E(x(X)) x E(X(x))

Let X1, , X, be iid with population pdf given by h ( which integrates to 1 over the real line. Here, the location parameter u E (-0, 00) and the scale parameter ao Denote log(h(z)) by (z). Denote the first and second derivatives of th by t and 3, respectively. where h is a positive twice-differentiable function a. Show that the score vector equals -- - () h Hence, or otherwise, show that E(O(X)) = 0 and E(Xp(X)) =-1 where the expectation here and below is calculated under the assumption that u 0 and o 1. S Show that the Fisher information matrix due to a single X is given by -E(x(X)) E(x(X)) x E(X(x))

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Let X1, , X, be iid with population pdf given by h ( which integrates to 1 over the real line. Here, the location parameter u E (-0, 00) and the scale parameter ao Denote log(h(z)) by (z). Denote the first and second derivatives of th by t and 3, respectively. where h is a positive twice-differentiable function a. Show that the score vector equals -- - () h Hence, or otherwise, show that E(O(X)) = 0 and E(Xp(X)) =-1 where the expectation here and below is calculated under the assumption that u 0 and o 1. S Show that the Fisher information matrix due to a single X is given by -E(x(X)) E(x(X)) x E(X(x))
Transcribed Image Text:Let X1, , X, be iid with population pdf given by h ( which integrates to 1 over the real line. Here, the location parameter u E (-0, 00) and the scale parameter ao Denote log(h(z)) by (z). Denote the first and second derivatives of th by t and 3, respectively. where h is a positive twice-differentiable function a. Show that the score vector equals -- - () h Hence, or otherwise, show that E(O(X)) = 0 and E(Xp(X)) =-1 where the expectation here and below is calculated under the assumption that u 0 and o 1. S Show that the Fisher information matrix due to a single X is given by -E(x(X)) E(x(X)) x E(X(x))
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