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0

$begingroup$

Could anyone explain me the equation below? Are we trying the find the T value where the $theta_T < E_0[t]?$

$T^* = underset{T}{Argmin} (theta_T geq E_0[T])$

I understand how argmin works for an equation like $underset{x}{Argmin} f(x)$. The question above is not a numeric solution (I think).

I would really appreciate if anyone can provide me guidance on this matter.

Thanks in advance!

statistics self-learning

share|cite|improve this question

edited 17 hours ago

boniface316

asked 18 hours ago

boniface316boniface316

1246

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The statement as it stands is very weird; it may mean that $T^star$ is the smallest $T$ such that $theta_T geq E_0[T]$. However, the notation $E_0[T]$ seems to indicate that $T$ is a random variable; could you give more context?
  $endgroup$
  – Riccardo Sven Risuleo
  17 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You are correct about the T being a random variable. I couldnt believe that answer was obvious! Thanks @RiccardoSvenRisuleo!
  $endgroup$
  – boniface316
  17 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not sure that that's the answer! As a matter of fact if T is a random variable, then $theta_T$ may also be a random variable; so the whole thing is a bit messy.
  $endgroup$
  – Riccardo Sven Risuleo
  17 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I can share the whole arguments if you would like....
  $endgroup$
  – boniface316
  17 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm just guessing, but if $theta_T$ is a random variable it may be that the expression is missing a probability? Something along the lines of $T^star = argmin_T P(theta_T geq E_0[T])$? Sadly, without reading the whole argument it is impossible to give a clear meaning to the statement.
  $endgroup$
  – Riccardo Sven Risuleo
  17 hours ago
  

  
  
  
  

add a comment | 

0

$begingroup$

Could anyone explain me the equation below? Are we trying the find the T value where the $theta_T < E_0[t]?$

$T^* = underset{T}{Argmin} (theta_T geq E_0[T])$

I understand how argmin works for an equation like $underset{x}{Argmin} f(x)$. The question above is not a numeric solution (I think).

I would really appreciate if anyone can provide me guidance on this matter.

Thanks in advance!

statistics self-learning

share|cite|improve this question

edited 17 hours ago

boniface316

asked 18 hours ago

boniface316boniface316

1246

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The statement as it stands is very weird; it may mean that $T^star$ is the smallest $T$ such that $theta_T geq E_0[T]$. However, the notation $E_0[T]$ seems to indicate that $T$ is a random variable; could you give more context?
  $endgroup$
  – Riccardo Sven Risuleo
  17 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You are correct about the T being a random variable. I couldnt believe that answer was obvious! Thanks @RiccardoSvenRisuleo!
  $endgroup$
  – boniface316
  17 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not sure that that's the answer! As a matter of fact if T is a random variable, then $theta_T$ may also be a random variable; so the whole thing is a bit messy.
  $endgroup$
  – Riccardo Sven Risuleo
  17 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I can share the whole arguments if you would like....
  $endgroup$
  – boniface316
  17 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm just guessing, but if $theta_T$ is a random variable it may be that the expression is missing a probability? Something along the lines of $T^star = argmin_T P(theta_T geq E_0[T])$? Sadly, without reading the whole argument it is impossible to give a clear meaning to the statement.
  $endgroup$
  – Riccardo Sven Risuleo
  17 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Could anyone explain me the equation below? Are we trying the find the T value where the $theta_T < E_0[t]?$

$T^* = underset{T}{Argmin} (theta_T geq E_0[T])$

I understand how argmin works for an equation like $underset{x}{Argmin} f(x)$. The question above is not a numeric solution (I think).

I would really appreciate if anyone can provide me guidance on this matter.

Thanks in advance!

statistics self-learning

share|cite|improve this question

edited 17 hours ago

boniface316

asked 18 hours ago

boniface316boniface316

1246

$endgroup$

share|cite|improve this question

edited 17 hours ago

boniface316

asked 18 hours ago

boniface316boniface316

1246

share|cite|improve this question

edited 17 hours ago

boniface316

asked 18 hours ago

boniface316boniface316

1246

asked 18 hours ago

boniface316boniface316

1246

asked 18 hours ago

boniface316boniface316

1246