Differentiating the expectation of the test function The 2019 Stack Overflow Developer Survey Results Are InIntegral with analytical solution with normal distributionLikelihood Ratio TestDifferentiating the posterior distribution functionDeriving most powerful test for hypothesisProving the Best Test for a Beta Distribution.Hypothesis testing with most powerful size $0.1$ testMost Powerful Test for Uniform DistributionPower function of a test,exampleBernoulli trials hypothesis testMonotone Likelihood ratio and Karlin-Rubin test
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Differentiating the expectation of the test function
The 2019 Stack Overflow Developer Survey Results Are InIntegral with analytical solution with normal distributionLikelihood Ratio TestDifferentiating the posterior distribution functionDeriving most powerful test for hypothesisProving the Best Test for a Beta Distribution.Hypothesis testing with most powerful size $0.1$ testMost Powerful Test for Uniform DistributionPower function of a test,exampleBernoulli trials hypothesis testMonotone Likelihood ratio and Karlin-Rubin test
$begingroup$
Question: Let $phi (X)$ be any test . Define $P_theta (X)=pdf(X;theta )$ and $dotP_theta (X)=fracmathrmd mathrmd theta pdf(X;theta )$ , then
$left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$
I don't know how to differentiate $E_theta phi (X)$ with respect to $theta$ and express it as the function of pdf even though the test funtion is not given. If $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$ is true, then can I say that $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]=E_theta [phi (X)dotP_theta (X)/P_theta (X)]$ for any test function $phi$ ?
statistics statistical-inference hypothesis-testing
asked Mar 30 at 11:21
LeeLee
1565
$endgroup$
add a comment |
$begingroup$
Question: Let $phi (X)$ be any test . Define $P_theta (X)=pdf(X;theta )$ and $dotP_theta (X)=fracmathrmd mathrmd theta pdf(X;theta )$ , then
$left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$
I don't know how to differentiate $E_theta phi (X)$ with respect to $theta$ and express it as the function of pdf even though the test funtion is not given. If $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$ is true, then can I say that $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]=E_theta [phi (X)dotP_theta (X)/P_theta (X)]$ for any test function $phi$ ?
statistics statistical-inference hypothesis-testing
asked Mar 30 at 11:21
LeeLee
1565
$endgroup$
add a comment |
$begingroup$
Question: Let $phi (X)$ be any test . Define $P_theta (X)=pdf(X;theta )$ and $dotP_theta (X)=fracmathrmd mathrmd theta pdf(X;theta )$ , then
$left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$
I don't know how to differentiate $E_theta phi (X)$ with respect to $theta$ and express it as the function of pdf even though the test funtion is not given. If $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$ is true, then can I say that $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]=E_theta [phi (X)dotP_theta (X)/P_theta (X)]$ for any test function $phi$ ?
statistics statistical-inference hypothesis-testing
asked Mar 30 at 11:21
LeeLee
1565
$endgroup$
Question: Let $phi (X)$ be any test . Define $P_theta (X)=pdf(X;theta )$ and $dotP_theta (X)=fracmathrmd mathrmd theta pdf(X;theta )$ , then
$left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$
I don't know how to differentiate $E_theta phi (X)$ with respect to $theta$ and express it as the function of pdf even though the test funtion is not given. If $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]_theta =theta _0=E_theta _0[phi (X)dotP_theta _0(X)/P_theta _0(X)]$ is true, then can I say that $left [ fracmathrmd mathrmd theta E_theta phi (X)right ]=E_theta [phi (X)dotP_theta (X)/P_theta (X)]$ for any test function $phi$ ?
statistics statistical-inference hypothesis-testing
statistics statistical-inference hypothesis-testing
asked Mar 30 at 11:21
LeeLee
1565
asked Mar 30 at 11:21
LeeLee
1565
asked Mar 30 at 11:21
LeeLee
1565
asked Mar 30 at 11:21
LeeLee
1565
asked Mar 30 at 11:21
LeeLee
1565
1565
add a comment |
add a comment |
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