Talk:Big O in probability notation

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Mathematics Mid‑priority

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Copied discussion[edit]

The following is copied for info from Wikipedia talk:WikiProject Statistics. Melcombe (talk) 09:38, 1 May 2009 (UTC) Op (statistics) is a very badly written article. Another article written by the same person, extremum estimator, suggests that "Op" is intended to be something akin to the big-O notation. But nothing in Op (statistics) explains that. Instead the article makes an assertion that is clearly not true as it stands. It never attempts to say what "Op" is. Can someone help? Michael Hardy (talk) 19:23, 29 April 2009 (UTC)[reply]

The idea is directly related to convergence in probability and might be best dealt with there perhaps (???) except that this redirects into a longer article (but this might still be suitable). Alternatively it could be put into the big-O notation article as it is almost a natural extension. The standard notation has a big or little O followed by a subscript p ... I think it is usually a lower case p but my dictionary uses a captial subscript P. A first problem would be to sort out a suitable article title even for a redirect .... the "p" or "P" stands for "probability" not "statistics". Melcombe (talk) 10:08, 30 April 2009 (UTC)[reply]

I have made some changes under the same title for the time being, but more work is needed, including finding a sensible title. Suggest move discussion to the article's talk page. Melcombe (talk) 11:41, 30 April 2009 (UTC)[reply]

Not sure if the definition of "big Oh p" is correct, seems to conflict with example I added? Biker333 (talk) 14:23, 22 August 2012 (UTC)[reply]

I don't really get the example but the definition is rather restrictive. A random sequence with the big Oh property shouldn't be bounded in the limit. It should have finite variance. For example, for a set of mean 0 iid random variables with finite variance, the sample mean is o_p(1) and O_p(n^(-1/2)) 19:21, 3 January 2013 (UTC) — Preceding unsigned comment added by 171.67.87.105 (talk)

"Big Oh p" and "little oh p" are related in a way to law of large numbers, central limit theorem, and Law of the iterated logarithm. 19:26, 3 January 2013

Comparison of the Two Definitions[edit]

In this section the author states that the distinction between little-Oh p and big-Oh p is subtle, depending only on the ordering of the conditions on epsilon, delta and n. This seems misleading to me. The distinction looks subtle because of the use of the same character, $\delta$ . The difference does not seem subtle: in little-Oh p the value $\delta$ (as written here) is approaching 0, while in big-Oh p, the $\delta$ is (or can) be very large but finite. (You don't see $\delta$ used in limit math to represent a very large number.) Without the confusion of using $\delta$ to represent a very large number, the putative subtlety disappears to my thinking. Anyone else agree? (I realize it's a subjective point) Chafe66 (talk) 03:51, 25 February 2015 (UTC)[reply]

Hi. I wrote that part but agree with you that the notion of "subtle/not obvious etc" is a subjective one. That distinction was not obvious to me (similarly to the difference between pointwise and uniform continuity), apparently it is more obvious for you. Surely it is difficult to know whether it will obvious or not be for the reader of the page, though I would rather go from the presumption that the reader is less familiar with the topic. Is your concern just about the use of the word subtle, or the use of the (akmost) same letter, or of the whole paragraph? If it is just the wording, you are welcome to change it, and if it is a more fundamental issue, we can discuss it further! — Preceding unsigned comment added by EtudiantEco (talk • contribs) 05:08, 27 February 2015 (UTC)[reply]

Probably too subjective to debate: you find the difference subtle, I do not. Since the existential quantifier is on

\delta _{\epsilon }

for the big-Oh definition, that number could be enormous, while for little-Oh, the

\delta

of interest is the infinitesimal one, not the enormous one. Bottom line for me I guess is that since the notion of "subtle" is indeed subjective, why not just leave it out? That way, if someone does find the distinction subtle, they're fine, and if someone does not find it subtle, also fine. If "subtle" is included, a person who really gets the notion might wonder if they're missing something when they don't find it subtle (like me). Chafe66 (talk) 21:16, 16 April 2015 (UTC)[reply]

New discussion[edit]

[1] contains definitions a little more careful and general than those here. McKay (talk) 13:25, 30 April 2009 (UTC)[reply]

Order of consistency of an estimator[edit]

It seems that the topic is directly related to that of the order of consistency of a statistical estimator. Maybe someone could add a precise statement to the article. Wurzel33 (talk) 19:32, 22 November 2013 (UTC)[reply]