Is strong law of large numbers an improvement of weak law of large numbers? [on hold]

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Is strong law of large numbers an improvement of weak law of large numbers ?

statistics statistical-inference information-theory

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asked Jan 27 at 19:45

MouliMouli

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put on hold as off-topic by user21820, RRL, Xander Henderson, José Carlos Santos, Saad yesterday

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• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, RRL, Xander Henderson, José Carlos Santos, Saad

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  Yes, that's why it's called strong.
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  – Robert Israel
  Jan 27 at 19:46
  

  
  
  
  


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  The conclusion is stronger, but it requires more stringent assumptions. In short: when both applies, the conclusion of the strong law is stronger than that of the weak law (unsurprisingly).
  $endgroup$
  – Clement C.
  Jan 27 at 19:47
  

  
  
  
  

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0

$begingroup$

Is strong law of large numbers an improvement of weak law of large numbers ?

statistics statistical-inference information-theory

share|cite|improve this question

asked Jan 27 at 19:45

MouliMouli

82

$endgroup$

put on hold as off-topic by user21820, RRL, Xander Henderson, José Carlos Santos, Saad yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, RRL, Xander Henderson, José Carlos Santos, Saad

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's why it's called strong.
  $endgroup$
  – Robert Israel
  Jan 27 at 19:46
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  The conclusion is stronger, but it requires more stringent assumptions. In short: when both applies, the conclusion of the strong law is stronger than that of the weak law (unsurprisingly).
  $endgroup$
  – Clement C.
  Jan 27 at 19:47
  

  
  
  
  

add a comment | 

0

0

0

$begingroup$

Is strong law of large numbers an improvement of weak law of large numbers ?

statistics statistical-inference information-theory

share|cite|improve this question

asked Jan 27 at 19:45

MouliMouli

82

$endgroup$

Is strong law of large numbers an improvement of weak law of large numbers ?

statistics statistical-inference information-theory

statistics statistical-inference information-theory

share|cite|improve this question

asked Jan 27 at 19:45

MouliMouli

82

share|cite|improve this question

asked Jan 27 at 19:45

MouliMouli

82

share|cite|improve this question

share|cite|improve this question

asked Jan 27 at 19:45

MouliMouli

82

asked Jan 27 at 19:45

MouliMouli

82

asked Jan 27 at 19:45

MouliMouli

82

82

put on hold as off-topic by user21820, RRL, Xander Henderson, José Carlos Santos, Saad yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, RRL, Xander Henderson, José Carlos Santos, Saad

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by user21820, RRL, Xander Henderson, José Carlos Santos, Saad yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, RRL, Xander Henderson, José Carlos Santos, Saad

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's why it's called strong.
  $endgroup$
  – Robert Israel
  Jan 27 at 19:46
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  The conclusion is stronger, but it requires more stringent assumptions. In short: when both applies, the conclusion of the strong law is stronger than that of the weak law (unsurprisingly).
  $endgroup$
  – Clement C.
  Jan 27 at 19:47
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's why it's called strong.
  $endgroup$
  – Robert Israel
  Jan 27 at 19:46
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  The conclusion is stronger, but it requires more stringent assumptions. In short: when both applies, the conclusion of the strong law is stronger than that of the weak law (unsurprisingly).
  $endgroup$
  – Clement C.
  Jan 27 at 19:47
  

  
  
  
  

$begingroup$
Yes, that's why it's called strong.
$endgroup$
– Robert Israel
Jan 27 at 19:46

$begingroup$
Yes, that's why it's called strong.
$endgroup$
– Robert Israel
Jan 27 at 19:46

3

3

$begingroup$
The conclusion is stronger, but it requires more stringent assumptions. In short: when both applies, the conclusion of the strong law is stronger than that of the weak law (unsurprisingly).
$endgroup$
– Clement C.
Jan 27 at 19:47

$begingroup$
The conclusion is stronger, but it requires more stringent assumptions. In short: when both applies, the conclusion of the strong law is stronger than that of the weak law (unsurprisingly).
$endgroup$
– Clement C.
Jan 27 at 19:47

add a comment | 

1 Answer
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The strong law of large numbers refers to almost sure convergence, while the weak law of large numbers corresponds to the convergence in probability.

The laws of large numbers are called strong and weak respectively because almost sure convergence implies convergence in probability, but the converse need not be true. Hence, we can say that the strong law is a strengthening of the weak law.

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edited Jan 28 at 18:30

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

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add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

0

$begingroup$

The strong law of large numbers refers to almost sure convergence, while the weak law of large numbers corresponds to the convergence in probability.

The laws of large numbers are called strong and weak respectively because almost sure convergence implies convergence in probability, but the converse need not be true. Hence, we can say that the strong law is a strengthening of the weak law.

share|cite|improve this answer

edited Jan 28 at 18:30

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

$endgroup$

add a comment | 

0

$begingroup$

The strong law of large numbers refers to almost sure convergence, while the weak law of large numbers corresponds to the convergence in probability.

The laws of large numbers are called strong and weak respectively because almost sure convergence implies convergence in probability, but the converse need not be true. Hence, we can say that the strong law is a strengthening of the weak law.

share|cite|improve this answer

edited Jan 28 at 18:30

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

$endgroup$

add a comment | 

0

0

0

$begingroup$

The strong law of large numbers refers to almost sure convergence, while the weak law of large numbers corresponds to the convergence in probability.

The laws of large numbers are called strong and weak respectively because almost sure convergence implies convergence in probability, but the converse need not be true. Hence, we can say that the strong law is a strengthening of the weak law.

share|cite|improve this answer

edited Jan 28 at 18:30

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

$endgroup$

The strong law of large numbers refers to almost sure convergence, while the weak law of large numbers corresponds to the convergence in probability.

The laws of large numbers are called strong and weak respectively because almost sure convergence implies convergence in probability, but the converse need not be true. Hence, we can say that the strong law is a strengthening of the weak law.

share|cite|improve this answer

edited Jan 28 at 18:30

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

share|cite|improve this answer

share|cite|improve this answer

edited Jan 28 at 18:30

edited Jan 28 at 18:30

edited Jan 28 at 18:30

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

answered Jan 27 at 19:50

Exp ikxExp ikx

4489

4489

add a comment | 

add a comment | 

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