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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Jarque-Bera test |

Date |
Thu, 27 Sep 2012 14:17:40 +0100 |

Excellent. Many thanks for pushing this forward. Nick On Thu, Sep 27, 2012 at 2:00 PM, Maarten Buis <maartenlbuis@gmail.com> wrote: > On Thu, Sep 27, 2012 at 3:44 AM, Nick Cox wrote: >> The essence of the matter is that Jarque-Bera uses asymptotic results >> regardless of sample size for a problem in which convergence to those >> results is very slow. This approach is decades out of date and I am >> surprised that StataCorp support the test without a warning. The >> Doornik-Hansen test, for example, looks much more satisfactory. > > I took up this challenge and did a simulation comparing the > performance of the Jarque-Bera test with the Doornik-Hansen test. In > particular I focused on whether the p-value follow a uniform > distribution, i.e. whether the nominal rejection rates correspond with > the proportion of simulations in which the test was rejected at those > nominal rates. In essence both tests perform badly at sample sizes of > a 100 and a 1,000. As Nick suggested, the Jarque-Bera test's > perfomance is more awful than the performance of the Doornik-Hansen > test, but for both tests my conclusion would be that a 1,000 > observations is just not enough for either test. At 10,000 and 100,000 > observations both tests seem to perform acceptable. However, at such > large sample sizes you need to worry about whether a rejection of the > null-hypothesis actually represents a substantively meaningful > deviation from the normal/Gaussian distribution. > > So the bottom line is: at small sample sizes graphs are the only > reliable way of judging whether a variable comes from a > normal/Gaussian distribution because tests just don't perform well > enough. At large sample sizes graphs are still the only reliable way > of judging whether a variable comes from a normal/Gaussian > distribution because in large sample sizes tests will pick up > substantively meaningless deviations from the null-hypothesis. > > *------------------- begin simulation ------------------- > clear all > > program define sim, rclass > drop _all > set obs `=1e5' > gen x = rnormal() > tempname jb jbp > forvalues i = 2/5 { > sum x in 1/`=1e`i'', detail > scalar `jb' = (r(N)/6) * /// > (r(skewness)^2 + 1/4*(r(kurtosis) - 3)^2) > scalar `jbp' = chi2tail(2,`jb') > return scalar jb`i' = `jb' > return scalar jbp`i' = `jbp' > > mvtest norm x in 1/`=1e`i'' > return scalar dh`i' = r(chi2_dh) > return scalar dhp`i' = r(p_dh) > > } > end > > simulate jb2=r(jb2) jbp2=r(jbp2) /// > jb3=r(jb3) jbp3=r(jbp3) /// > jb4=r(jb4) jbp4=r(jbp4) /// > jb5=r(jb5) jbp5=r(jbp5) /// > dh2=r(dh2) dhp2=r(dhp2) /// > dh3=r(dh3) dhp3=r(dhp3) /// > dh4=r(dh4) dhp4=r(dhp4) /// > dh5=r(dh5) dhp5=r(dhp5) /// > , reps(2e4): sim > > rename jbp2 p2jb > rename jbp3 p3jb > rename jbp4 p4jb > rename jbp5 p5jb > rename dhp2 p2dh > rename dhp3 p3dh > rename dhp4 p4dh > rename dhp5 p5dh > > gen id = _n > > reshape long p2 p3 p4 p5, i(id) j(dist) string > > label var p2 "N=100" > label var p3 "N=1,000" > label var p4 "N=10,000" > label var p5 "N=100,000" > > encode dist, gen(distr) > label define distr 2 "Jarque-Bera" /// > 1 "Doornik-Hansen", replace > label value distr distr > > simpplot p?, by(distr) scheme(s2color) legend(cols(4)) > *-------------------- end simulation -------------------- > (For more on examples I sent to the Statalist see: > http://www.maartenbuis.nl/example_faq ) > > This simulation requires the -simpplot- package available at SSC and > described here: <http://www.maartenbuis.nl/software/simpplot.html> > > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Jarque-Bera test***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: Jarque-Bera test***From:*Maarten Buis <maartenlbuis@gmail.com>

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