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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Testing for differences in skewness and kurtosis? |

Date |
Sat, 5 May 2012 17:34:09 +0100 |

-lmoments- (SSC) offers alternative measures of skewness and kurtosis. They behave much better than moment-based measures. But I don't see that they fit with the approach George is taking. Nick On Sat, May 5, 2012 at 5:29 PM, Cameron McIntosh <cnm100@hotmail.com> wrote: > A bootstrap approach might indeed be palatable here. On that note, I would suggest perhaps looking into the literature on skewness persistence (in which robust measures of both skewness and kurtosis have been developed): > > Ergun, A.T. (June 13, 2011). Skewness and Kurtosis Persistence: Conventional vs. Robust Measures. Midwest Finance Association 2012 Annual Meetings Paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1857653 > > Muralidhar, K. (1993). The Bootstrap Approach for Testing Skewness Persistence. Management Science, 39(4), 487-491. > > Nath, R. (1996). A Note on Testing for Skewness Persistence. Management Science, 42(1), 138-141. > > Sun, Q., & Yan, Y. (2003). Skewness persistence with optimal portfolio selection. Journal of Banking & Finance, 27(6), 1111–1121. > > Adcock, C.J., & Shutes, K. (2005). An analysis of skewness and skewness persistence in three emerging markets. Emerging Markets Review, 6(4), 396–418. >> Date: Sat, 5 May 2012 17:05:16 +0100 >> Subject: Re: st: Testing for differences in skewness and kurtosis? >> From: njcoxstata@gmail.com >> To: statalist@hsphsun2.harvard.edu >> >> I'll add a >> >> 6. You could also end up showing that skewness and kurtosis are >> similar but both imply non-normality. That would also undermine your >> tests based on normality. Only one possible outcome of the tests, that >> skewness and kurtosis are similar and results for both imply >> approximate normality would be entirely good news for you. >> >> >> On Sat, May 5, 2012 at 4:33 PM, Nick Cox <njcoxstata@gmail.com> wrote: >> > This question provokes various comments from me. They are all >> > variations on a single theme, that this is much more problematic than >> > you imply. >> > >> > 1. Large-sample standard errors for skewness and kurtosis _if_ the >> > parent is normal are given in many mathematical statistics texts and >> > could be the basis for a test. But if the normality of the >> > distributions is even slightly in doubt I have the impression that >> > they aren't worth much. Even if it is not in doubt, the large-sample >> > results do not kick in quickly. (There is at least one command in >> > official Stata that is wildly cavalier about this point! Some >> > economists use the so-called Jarque-Bera test based on asymptotic >> > standard errors as a test for normality.) >> > >> > 2. This is linked to the fact that skewness and kurtosis, as dependent >> > on third and fourth powers of deviations from the mean, can be very >> > sensitive to departures of any kind. I don't know in consequence what >> > a robust test of skewness and kurtosis would look like; that sounds a >> > contradictory request to make. If you are interested in robust >> > comparisons, skewness and kurtosis are not where you start. >> > >> > 3. You sound very confident that your distributions are normal but >> > with real data that is at best an approximation. It is an >> > approximation that you can get away frequently with tests on means, >> > less frequently with tests on variances, and even less frequently with >> > higher moments. Box in Biometrika 1953 remains pertinent. >> > >> > 4. Let's imagine that you applied such a test. As parent normals both >> > have skewness 0 and kurtosis 3, a difference in skewness or kurtosis >> > between two samples would be likely to arise if at least one >> > distribution was really not normal. This is just a restatement of the >> > fact that if two quantities are different, they can't be equal, and so >> > not equal to any particular constant. So, you would need to consider >> > that possibility of non-normality directly. If you concluded that that >> > was so, you could end up undermining the results of your previous >> > tests. So, I don't think you can ignore the question of whether the >> > samples come from the same distribution. It's an assumption behind >> > what you are doing, even if it is not independently interesting. >> > >> > 5. In some ways the most direct way to compare skewness and kurtosis >> > would be to bootstrap, but that would ignore the question of whether >> > the distributions are normal, which is a crucial assumption so far as >> > you are concerned. Perhaps better is to simulate normal samples with >> > the same sizes, means and SDs. >> > >> > When you have two distributions, a -qqplot- is a restatement of _all_ >> > the information on those distributions. It would throw light on >> > whether apparent non-normal skewness or kurtosis arises from >> > individual outliers or something more systematic. >> > >> > Nick >> > >> > Box, G.E.P. 1953. Non-normality and tests on variances. Biometrika 40: 318-335. >> > >> > On Sat, May 5, 2012 at 3:34 PM, George Murray <george.murray16@gmail.com> wrote: >> > >> >> I am currently working with a very simple dataset, with two variables, >> >> V0 and V1 (around 150 obs each), each normally distributed, and the >> >> difference of the means of the distribution of the variables are >> >> (statistically) different, but the standard deviations are equal. I >> >> would like to test whether there exists any significant difference in >> >> the skewness of these two variables. Can this be done through >> >> hypothesis testing, or is this only possible through some simulation >> >> technique (bootstrapping?) Is there a test that is robust to the >> >> aforementioned conditions? Is there an equivalent test for kurtosis? >> >> Is anyone aware of how this can be calculated with Stata? (And no, I >> >> am not trying to test whether they come from the same distribution) * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Testing for differences in skewness and kurtosis?***From:*George Murray <george.murray16@gmail.com>

**Re: st: Testing for differences in skewness and kurtosis?***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: Testing for differences in skewness and kurtosis?***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: Testing for differences in skewness and kurtosis?***From:*Cameron McIntosh <cnm100@hotmail.com>

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