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Point estimator as a vector

Point Estimator.Compute the Maximum Likelihood Estimator of a pareto Distribution for statistic…Maximum Likelihood without density?How to compute the consistency of an estimatorHow to show an estimator is consistent and solve the asymptotic distribution?Derive an unbiased estimator for $theta$.Does this estimator respect the likelihood principle?Understanding the density function and expected value of an estimator.Proving that the average of a log-likelihood ratio involving an ML estimator is positiveDerived parameter instead of parameter estimation

0

$begingroup$

I am given the following definition of a point estimator.

Definition: $hattheta$ is point estimator of $theta$ if $hattheta = g(X_1,...,X_n)$ where $X_1,...,X_n$ are iid distributed with parameter $theta$ and $g$ is some function that estimates $theta$.

My question is whether this definition implies that we are only considering $thetain mathbbR$ (since a function is not a vector) instead of $theta in mathbbR^m$ which is in general the case.

statistical-inference

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edited yesterday

Dani

asked yesterday

DaniDani

30411

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The definition is in general $m$ dimensional since a function can be a vector, i.e., $g:mathbbR^ntomathbbR^m$ in general. It usually coincides with the dimensionality of $X_1$ or maybe you could have a function which estimates both parameters of a Gamma distribution for example.
  $endgroup$
  – Stan Tendijck
  yesterday
  

  
  
  
  

add a comment | 

0

$begingroup$

I am given the following definition of a point estimator.

Definition: $hattheta$ is point estimator of $theta$ if $hattheta = g(X_1,...,X_n)$ where $X_1,...,X_n$ are iid distributed with parameter $theta$ and $g$ is some function that estimates $theta$.

My question is whether this definition implies that we are only considering $thetain mathbbR$ (since a function is not a vector) instead of $theta in mathbbR^m$ which is in general the case.

statistical-inference

share|cite|improve this question

edited yesterday

Dani

asked yesterday

DaniDani

30411

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The definition is in general $m$ dimensional since a function can be a vector, i.e., $g:mathbbR^ntomathbbR^m$ in general. It usually coincides with the dimensionality of $X_1$ or maybe you could have a function which estimates both parameters of a Gamma distribution for example.
  $endgroup$
  – Stan Tendijck
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

I am given the following definition of a point estimator.

Definition: $hattheta$ is point estimator of $theta$ if $hattheta = g(X_1,...,X_n)$ where $X_1,...,X_n$ are iid distributed with parameter $theta$ and $g$ is some function that estimates $theta$.

My question is whether this definition implies that we are only considering $thetain mathbbR$ (since a function is not a vector) instead of $theta in mathbbR^m$ which is in general the case.

statistical-inference

share|cite|improve this question

edited yesterday

Dani

asked yesterday

DaniDani

30411

$endgroup$

share|cite|improve this question

edited yesterday

Dani

asked yesterday

DaniDani

30411

share|cite|improve this question

edited yesterday

Dani

asked yesterday

DaniDani

30411

asked yesterday

DaniDani

30411

asked yesterday

DaniDani

30411