Confidence interval for interquartile range

[Olga Goldfine]

Dear Statalist members, I would be most thankful for an advice. I need to estimate the confidence intervals for interquartile range. As a first step, I use the interquartile regression, and predict option to get iqr and standard deviation.

iqreg y i.x , reps(100)

predict iqr_est
predict iqr_est_sd, stdp

This gives me, as I understand the bootstrapped estimate of the IGR and the SD. However, I am at loss how to get a good estimate of confidence interval. Would be very thankful for any tip!

[FernandoRios]

Hi Olga,
What exactly is what you are trying to estimate the Confidence interval for?
The interquantile range, conditional for characteristics? or the interquantile rage over the whole distribution?
Fernando

[Olga Goldfine]

Hi Fernando, thank you for your answer - and the good question! I need the confidence bands for the second - the interquantile range over the distribution.

[Mike Lacy]

If you want the CI for the IQR of the overall distribution, then you don't want/need -iqreg-. Rather, you need some program that produces the iqr as a descriptive statistic. The simplest command I could figure out to use was -tabstat- and extract the iqr from the return list matrix in which it is returned, which requires the modestly obscure function el(MatrixName, Row, Col) . Perhaps there is a more straightforward way to get the IQR as a descriptive statistic in a directly accessible form, but I don't happen to know it:

tabstat y, stat(iqr) // get the descriptive stat
bootstrap iqr = el(r(StatTotal), 1, 1), reps(1000): tabstat y, stat(iqr) save 
mat list e(ci_percentile) //display the CI

I'd use the percentile CI rather than the normal approximation because I doubt very much that the sampling distribution of the IQR is normal.

[FernandoRios]

In addition to Mike's Advice, i would also say that iqreg can be used for the same purpose

webuse nlswork, clear
bootstrap iqr = el(r(StatTotal), 1, 1), reps(100) seed(100): tabstat ln_wage, stat(iqr) save
iqreg ln_wage,  q(25 75)
*or bootstrapping the iqreg. This will be much slower tho
bootstrap, reps(100) seed(100):iqreg ln_wage,  q(25 75)

[Olga Goldfine]

Thank you very much for your generous and quick help!