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Minimum sufficient statistic for logistic regression model

Sufficient statistic for normal distribution with known mean.Creating a minimal sufficient statistic with Likelihood functionHow do i know what's the sufficient statistic/estimator?What is a sufficient statistic of this distribution?Derive a sufficient statistic for $theta$.Sufficient statistic with…Minimal sufficient statistic for normal distribution with known varianceMinimal sufficient statistic for $theta$ where $f(x;theta)$ = $2(1+theta-x) I_theta le x letheta+1$Proving that a minimal sufficient statistic is not completeThe natural sufficient statistic is minimal sufficient

0

$begingroup$

For the question in the link below, I am seeking the minimal sufficient statistic for $theta$=$beta_1$,$beta_2$ in the linear regression model given.

I have taken the ratio of likelihoods $L(x, theta)$/$L(y,theta)$ which has given me the result below:

I know that I am looking for a condition that makes the likelihood ratio independent of $theta$. From the first term in the product, when the sum of all $x_i$ is equal to the sum of all $y_i$, this term is made independent of $theta$.

What about the second term in this product? Is there a second condition from this fraction that I need to synthesise into the solution, or have I already shown that the minimal sufficient statistic is the sum of all $x_i$? I can't find a way to algebraically break up that second fraction so that the product symbol goes away on each side.

Thanks.

statistical-inference logistic-regression data-sufficiency

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edited Mar 11 at 8:39

CaptainQwark

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12

New contributor

CaptainQwark is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment | 

0

$begingroup$

For the question in the link below, I am seeking the minimal sufficient statistic for $theta$=$beta_1$,$beta_2$ in the linear regression model given.

I have taken the ratio of likelihoods $L(x, theta)$/$L(y,theta)$ which has given me the result below:

I know that I am looking for a condition that makes the likelihood ratio independent of $theta$. From the first term in the product, when the sum of all $x_i$ is equal to the sum of all $y_i$, this term is made independent of $theta$.

What about the second term in this product? Is there a second condition from this fraction that I need to synthesise into the solution, or have I already shown that the minimal sufficient statistic is the sum of all $x_i$? I can't find a way to algebraically break up that second fraction so that the product symbol goes away on each side.

Thanks.

statistical-inference logistic-regression data-sufficiency

share|cite|improve this question

edited Mar 11 at 8:39

CaptainQwark

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12

New contributor

CaptainQwark is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

For the question in the link below, I am seeking the minimal sufficient statistic for $theta$=$beta_1$,$beta_2$ in the linear regression model given.

I have taken the ratio of likelihoods $L(x, theta)$/$L(y,theta)$ which has given me the result below:

I know that I am looking for a condition that makes the likelihood ratio independent of $theta$. From the first term in the product, when the sum of all $x_i$ is equal to the sum of all $y_i$, this term is made independent of $theta$.

What about the second term in this product? Is there a second condition from this fraction that I need to synthesise into the solution, or have I already shown that the minimal sufficient statistic is the sum of all $x_i$? I can't find a way to algebraically break up that second fraction so that the product symbol goes away on each side.

Thanks.

statistical-inference logistic-regression data-sufficiency

share|cite|improve this question

edited Mar 11 at 8:39

CaptainQwark

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12

New contributor

CaptainQwark is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 11 at 8:39

CaptainQwark

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12

New contributor

CaptainQwark is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 11 at 8:39

CaptainQwark

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12

New contributor

CaptainQwark is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12

New contributor

CaptainQwark is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 11 at 8:05

CaptainQwarkCaptainQwark

12