Talk:Heteroscedasticity

ossible heteroskedasticity of residuals can be find by using White's Heteroskedasticity Test on data. Heteroskedasticity problem can be avoided using Weighted Least Squares (WLS)-regression instead of Ordinary Least Squares (OLS)-regression.

added, gtx, Frank1101 19:47, 26 July 2006 (UTC)

sources not named

White (1980).

Could you expand on this comment? I am not sure what you are getting at. --Richard Clegg 13:02, 26 July 2006 (UTC)

spelling

quote: (There seems to be no standard agreed-upon spelling for these words; they are sometimes spelled homo- or heteroscedastic or -schedastic, depending on location and personal taste.)

schedastic: I have never seen this, is this a valid spelling? I'm not a native speaker... Gtx, Frank1101 21:34, 16 September 2006 (UTC)

We think it is good to mention alternate spellings. But the second sentence seems more like an observation rather than fact, and doesn't add to the discussion at hand. Unless its deemed relevant or links to American vs. British spellings is warranted, this could probably be cut out.

Ref.: (In America, it is usually spelled homoscedastic. It is an exception to the rule that American spellings are usually more faithful to the etymologies than British spellings.)

I would like to draw your attention to McCulloch, J. H.: "On Heteros*edasticity", Econometrica, vol. 53, no. 2, March 1985, pp. 403. The author explores the linguistic aspects, and makes it very clear that "Heteroskedasticity is therefore the proper English spelling." -80.145.78.164 14:15, 2 January 2007 (UTC)

my econometrics book spells it heteroskedasticity as well 71.83.122.143 06:45, 13 April 2007 (UTC)

I haven't found the corresponding line yet but Peter Kennedy also made a clear statement and gives reliable sources in his book "A Guide to Econometrics" that "heteroskedasticity" with "k" is the correct spelling. -- MM-Stat (talk) 14:38, 1 February 2010 (UTC)

In Greene (5th, 6th, and 7th editions) and Wooldridge, and in statistical programs like Stata, R, and SAS, I have only seen it spelled heteroskedasticity 207.55.8.2 (talk) 20:53, 24 January 2012 (UTC)

I'm looking at Greene 5th edition right now - it's spelled with "c". That said, every other book I can put my hands on right now (Wooldridge, Kennedy, Griffiths Hill & Judge, Cameron & Trivedi, Stock & Watson) spell it with a "k" except Greene and Gujarati & Porter. And both of those are newer editions of 25-year-old textbooks. DaveDixon (talk) 16:15, 19 April 2015 (UTC)

Just saw the table of contents for the 7th edition on Greene's web page: still spelt with "c". DaveDixon (talk) 19:05, 19 April 2015 (UTC)

(unsigned contribution) Paper explaining the preferred spelling: http://www.ime.usp.br/~abe/lista/pdfZAptC9KazU.pdf ( end unsigned contribution) Note that this is the McCulloch, in Econometrica, referred to above. Melcombe (talk) 17:19, 7 February 2012 (UTC)

All my life in college and university, I have always encountered in books and myself used only "heterosKedasticity" - came today to this article and was totally surprised by the spelling...

merge

There's an article called heteroscedacity, which seems not a Yank-v-Brit difference, but a simple misspelling in any country. It seems a good bit less complete than this article, but maybe someone else would like to take a look to see if anything should be merged from it before it's redirected here. --Trovatore 07:00, 21 December 2005 (UTC)

I'm not so sure that spelling with a c is the incorrect version - it was certainly how I learned it. A literature search on PubMed for 'heteroscedastic' gives 82 results compared to only 10 for 'heteroskedastic', 'heteroscedasticity' gives 67 items whereas 'heteroskedasticity' gives 17. --84.12.32.134 18:41, 27 December 2005 (UTC)

The issue isn't c or no c. The c-vs-k thing is a Yank/Brit difference and falls under the usual rules (since this isn't specific to a country or culture, the first article written gets to keep its spelling). The misspelling is "heteroscedacity" (ends in -acity when it should end in -asticity). --Trovatore 18:59, 27 December 2005 (UTC)

Homoscedasticity exists, and is so spelt. Wikipedia is inconsistent, but this seems excessive. I prefer -sced- as the usual treatment of Greek names. Is there objection to moving this article? Septentrionalis 18:01, 6 October 2006 (UTC)

online link to that reference is here [1] Justinc (talk) 15:46, 15 November 2011 (UTC)

A search on scholar.google.com yields 109,000 hits for "heteroskedasticity" (2330 since 2015) versus 95,700 for "heteroscedasticity" (2220 since 2015). Not decisive, but far different from the PubMed result. DaveDixon (talk) 16:21, 19 April 2015 (UTC)

Most of the links to here

Use the -k spelling. After years of statistics, this is the first place I've ever seen it spelled with a -c. Jarring, to say the least. 170.140.214.100 18:28, 2 December 2007 (UTC)

You haven't been around much. Michael Hardy (talk) 05:17, 20 August 2008 (UTC)

Seriously use -k. I refer you again to the Econometrica publication by McCulloch. I am certain that trumps all of your other banter. Brit, Yank, whoever will certainly agree that Econometrica knows what it is talking about in regards to statistics.128.146.137.125 (talk) 19:36, 29 March 2008 (UTC)

Improving the illustration

There is an illustration in the article showing an example of heteroscedasticity, and as someone new to the topic it would be helpful to my understanding if some (simple) formula for generating such a plot were provided in conjunction with the plotted output, along with the actual values of the variables along the x-axis (e.g. one colored line per variable, similarly colored in the formula). Similarly, the plot illustrated for homoscedasticity could be updated so that by comparison it's easy to see the difference in the variances of the variables affecting the output. —Preceding unsigned comment added by 209.203.104.2 (talk) 18:47, 30 January 2008 (UTC)

clarified statement of importance

i have reworded the second paragraph for clarity: heteroskedasticity is not a significant concern *of* regression analysis (that connotes regression analysis is principally used to study heteroskedasticity); "bad effect" means the statistical tests are uninterpretable (rather than incalculable); the tests are uninterpretable *because* the statistical distributions used to calculate the area probabilities may no longer apply. 67.142.161.19 (talk) —Preceding undated comment added 18:01, 24 September 2011 (UTC).

Heteroskedasticity does not cause bias

The presence of heteroskedasticity in a dataset does not cause OLS estimators to be bias, only inefficient. Should be changed.

I have changed the entry because this comment is completly true: OLS is still (conditionally) unbiased, consistent and asintotically normal under heteroskedaticity. —Preceding unsigned comment added by Heteroskedasticity (talk • contribs) 02:51, 21 April 2010 (UTC)

Rank correlation for testing heteroscedasticity?

On Feb 19th, 2010, somebody added the rank correlation as a test for chekcing heteroscedasticity. Anyone has any reference about how that is done? I am unable to find any such reference. Otherwise, I think this test should be deleted. —Preceding unsigned comment added by Samikrc (talk • contribs) 15:09, 25 June 2010 (UTC)

this page is far too specialized and unclear. Please revise 134.174.110.6 (talk) 17:14, 5 November 2010 (UTC)

Clarification - check accuracy

The text used to read: "Most of the methods of detecting heteroscedasticity outlined above modified for use even when the data do not come from a normal distribution.". I changed it to " Most of the methods of detecting heteroscedasticity outlined above can be modified for use even when the data do not come from a normal distribution." - Please confirm that this is correct. --Slashme (talk) 13:59, 20 August 2013 (UTC)

Etymology.

Could some editor add etymology. What (most likely Greek) words are etymons of this word?

Just noticed the info was there. I separated it in a section so that it looks similar to many other articles in Wikipedia.

Dr. Santos Silva's comment on this article

Dr. Santos Silva has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

The existence of heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, as it can invalidate statistical tests of significance that assume that the modelling errors are uncorrelated and uniform—hence that their variances do not vary with the effects being modeled.

- "uncorrelated and uniform" is incorrect; it should be "uncorrelated and homoskedastic"

For instance, while the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient because the true variance and covariance are underestimated.

- "because the true variance and covariance are underestimated" is incorrect; it should be "For instance, while the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and estimated covariance of the estimator is invalid."

Because heteroscedasticity concerns expectations of the second moment of the errors, its presence is referred to as misspecification of the second order.

- The paragraph above should be deleted.

In dealing with conditional expectations of Yt given Xt,

- This is wrong; it should be "In dealing with conditional distribution of Yt given Xt, "

is said to be heteroscedastic if the conditional variance of Yt given Xt, changes with t.

- This is wrong; it should be "changes with Xt"

- The rest of the article is not particularly good, but I did not find more glaring errors

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Santos Silva has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : J. M. C. Santos Silva & Silvana Tenreyro, 2009. "Further Simulation Evidence on the Performance of the Poisson Pseudo-Maximum Likelihood Estimator," CEP Discussion Papers dp0933, Centre for Economic Performance, LSE.

ExpertIdeasBot (talk) 11:03, 28 May 2016 (UTC)

I saw the mistake about the definition too and wondered if I'd forgotten my basic econometrics. The classic example of heteroskedasticity is when the variance of the disturbance term is bigger if the value of X is bigger.-- but in that case the variance *conditional on X* is the same across all observations. See http://www3.wabash.edu/econometrics/EconometricsBook/chap19.htm . I probably count as an expert too, as a PhD economist.

--editor3 04:19, 18 April 2020 (UTC)

Dr. Reed's comment on this article

Dr. Reed has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

An omission under "Fixes" is to include the following reference: Wooldridge, J. Introductory Econometrics, Sixth Edition, Cengage Learning, 2016, pages 259-264.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Reed has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Xiujian Chen & Shu Lin & W. Robert Reed, 2006. "A Monte Carlo Evaluation of the Efficiency of the PCSE Estimator," Working Papers in Economics 06/14, University of Canterbury, Department of Economics and Finance.

ExpertIdeasBot (talk) 16:07, 12 July 2016 (UTC)

Further reading and external links

The further reading and external link lists consist exclusively of material from econometrics. Development of those lists could include general statistics texts as well as representation of other fields that use regression or are otherwise concerned with heteroscedasticity. Mw011235 (talk) 01:19, 26 January 2017 (UTC)

You can't do hypothesis testing wit h the OLS estimator really, can you?

"This validates the use of hypothesis testing using OLS estimators and White's variance-covariance estimator under heteroscedasticity."

This seems wrong. If you use White's estimator, which is NOT OLS, you can do hypothesis testing, but not just with OLS, because you have biased standard errors. Right?editeur24 (talk) 02:50, 16 April 2021 (UTC)

While you're technically correct, it's an abuse of nomenclature. The ordinary least squares estimator solves the least squares problem. It doesn't make much sense to associate the name "OLS" with a variance-covariance matrix estimator. --bender235 (talk) 17:01, 18 April 2021 (UTC)

Some rewriting might be helpful in the article. Here's my latest thinking. The OLS estimated coefficient is unbiased. The OLS standard errors are biased. The White standard errors are consistent, at least, so there's a good argument for using them. So you could use the OLS coefficient and the White standard errors and that is okay. Better yet, you could use the White variance matrix to estimate the coefficients too, and then you've done even better. But it's kind of strange to stop with just using OLS coefficients and White standard errors.

One thing that confuses me and will confuse non-expert readers even more is the difference between unbiasedness and consistency. They're both good, but they're different, and consistency only *really* applies to infinite samples. I don't remember: is the White variance estimate unbiased? Does it need a degrees of freedom correction to be unbiased? I'd more confidently guess that the White coefficient estimator is unbiased, since it just weights the observations-- right?--- but maybe I'm wrong on that. Or am I completely off base and there is no White coefficient estimator, just White standard errors? In any case, I hope some econometrician reads this and uses it as evidence of what a semi-sophisticated reader is wanting to get out of the article.editeur24 (talk) 16:00, 19 April 2021 (UTC)

Merger

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

Consensus to merge Homoscedasticity and Heteroscedasticity to Homoscedasticity and heteroscedasticity. Felix QW (talk) 14:22, 14 May 2022 (UTC)

---

Homoscedasticity and Heteroscedasticity are simply reciprocals. fgnievinski (talk) 07:41, 3 October 2021 (UTC)

Support. – Seems highly unlikely somebody would want to know about one without also knowing about the other. Since when you are testing if your data shows homoscedasticity you are implicitly checking whether it shows heteroscedasticity. Even for Type I and type II errors, which are not as directly reciprocal, we have a single page. Gazelle55 (talk) 19:21, 5 October 2021 (UTC)

Support. - Agree with above. They are reciprocals and an average reader using the Wiki would want to know about both. Both pages are also relatively small so it shouldn't be two large of a merge. 114.110.37.224 (talk) 21:55, 2 February 2022 (UTC)

Support. - The concepts are too intertwined, and are not separable; having two pages to describe them is redundant. I cannot imagine that that they will remain this way, or any conceivable rationale for opposing this merge.SpiralSource (talk) 10:47, 14 March 2022 (UTC)

Support I think the ways that heteroscedasticity isn't simply reciprocal to homoscedasticity can get their own page (e.g. GARCH). Protonk (talk) 16:12, 14 March 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.