Timeline for Counterexample for the sufficient condition required for consistency
Current License: CC BY-SA 3.0
12 events
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
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| Sep 25, 2015 at 19:04 | comment | added | cardinal | @Silverfish: Thanks for the heads-up. Since commenters don't receive notification of subsequent edits, things can get out-of-date. Usually, this is of little consequence, but I agree here that the prominence of that comment is pretty misleading. I've deleted it. Cheers. | |
| Sep 25, 2015 at 18:44 | comment | added | Alecos Papadopoulos | @Silverfish Cardinal's comment indeed refers to my initial answer (the part under the grey bar near the end of the post). Exactly because this initial answer generated comments that are still present, I have left it un-deleted, below the new answer. I added something on the grey bar to help a bit with the confusion. | |
| Sep 25, 2015 at 18:43 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
Added administrative clarification
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| Sep 25, 2015 at 17:17 | comment | added | Silverfish | @cardinal If you no longer believe the current answer to be incorrect, perhaps you could delete your comment, or post a fresh comment to confirm that the current answer no longer is incorrect? From a reader's point of view, having an upvoted answer saying that an answer is incorrect is confusing (and forces one to start checking the edit chronologies). | |
| Jan 31, 2014 at 19:14 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
typos
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| Jan 31, 2014 at 17:53 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
deleted 3 characters in body
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| Jan 31, 2014 at 16:03 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
Offered a new answer, responding to comments
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| Jan 31, 2014 at 13:39 | comment | added | KOE | I put an example of convergence in probability with always positive, finite variance in my answer here as well. | |
| Jan 31, 2014 at 11:22 | comment | added | cardinal | The example I gave in the comment linked to in my note to the OP has finite limiting variance. Consistency deals with convergence in probability, which you've correctly noted. But for the variance to go to zero, we have to control the tails (too). This is related to the relationship between $L_p$ convergence and convergence in probability. | |
| Jan 31, 2014 at 7:13 | comment | added | Alecos Papadopoulos | @cardinal Thanks for the intervention, and I will be happy to correct it. Can I have a hint on how could I start looking for a consistent estimator whose variance converges to a finite number? (The infinite/undefined variance case is a known case and should have been mentioned -but the finite non-zero case is the really interesting one). Or did I describe the property of consistency wrongly? | |
| Jan 31, 2014 at 0:19 | history | answered | Alecos Papadopoulos | CC BY-SA 3.0 |