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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.
White (1980).
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)
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)
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...
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)
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)
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)
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)
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).
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)
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)
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)
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 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:
ExpertIdeasBot ( talk) 11:03, 28 May 2016 (UTC)
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:
ExpertIdeasBot ( talk) 16:07, 12 July 2016 (UTC)
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)
"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)
Homoscedasticity and Heteroscedasticity are simply reciprocals. fgnievinski ( talk) 07:41, 3 October 2021 (UTC)
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A graph should have been displayed here but
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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.
White (1980).
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)
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)
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...
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)
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)
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)
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)
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).
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)
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)
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)
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 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:
ExpertIdeasBot ( talk) 11:03, 28 May 2016 (UTC)
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:
ExpertIdeasBot ( talk) 16:07, 12 July 2016 (UTC)
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)
"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)
Homoscedasticity and Heteroscedasticity are simply reciprocals. fgnievinski ( talk) 07:41, 3 October 2021 (UTC)