mayer79 / confintr Goto Github PK

Hi @mayer79, I noticed that the student bootstrapped CIs for skewness and kurtosis are provided in DescTools as their standard error formulae are given in the script of DescTools::Skew() and DescTools::Kurt(). You could consider incorporating this bootstrap option. Also note that DescTools has three methods of calculating skewness and kurtosis each, with the default method = 3 different from the typical definition as in method = 1. I have not investigated how the three methods compare with each other.

There is a mistake in the studentized bootstrap CIs for

• ci_mean()
• ci_mean_diff()
• ci_var()
• ci_sd(), and
• ci_proportion()

Mainly affected are the first two function, because there, studentized bootstrap is the default bootstrap method.

The problem: boot::boot() expects as second component a function for the variance, not for the standard deviation of the estimator. This will lead to wrong reference distributions and thus, to wrong confidence intervals.

Problem with Latex text in MacOS

Fixed in #15

We need better unit tests, especially for the Bootstrap confidence intervals.

Hi @mayer79, would you consider adding function for confidence intervals of variance and standard deviation ratio and difference between two (independent) samples? I once wrote R functions that calculate student and percentile bootstrap confidence intervals of standard deviation ratios between two independent samples, based on both raw ratio and its logarithm. I do not think the asymptotic "normal" bootstrap is appropriate, as the ratios are usually skewed. It is probably better to generate confidence intervals of variance ratios first, then transform them to those of standard deviation ratios. I assume the logarithm of a ratio is less skewed than its raw form and possibly has a better property when forming confidence intervals, but I have not explored its theoretic or empirical basis. I can show my script if needed.

The following sources might be helpful

• Asymptotic distribution of sample variance of non-normal sample relative to the population mu and sigma. https://stats.stackexchange.com/questions/105337.
• UW Matlab Example 3: Bootstrapping on a ratio of variances https://courses.washington.edu/matlab1/Bootstrap_examples.html#13
• Standard error of a ratio https://stats.stackexchange.com/questions/21167
• Variance of the reciprocal II https://stats.stackexchange.com/questions/19576
• Testing the significance of differences between ratios with small samples https://stats.stackexchange.com/questions/12069
• Kim, J. H. (2006). Wild bootstrapping variance ratio tests. Economics Letters, 92(1), 38–43. https://doi.org/10.1016/j.econlet.2006.01.007
• SE of variance and SD: https://stats.stackexchange.com/questions/156518

Hi @mayer79, I wonder if bias-corrected and accelerated (BCA) bootstrapping performs better than student bootstrapping on confidence intervals of variance, standard deviation, and proportion. I loved your package for including student bootstrap confidence intervals, as it is rarely directly available in other packages.

I noticed that the default bootstrap method for variance, standard deviation, and proportion is the BCA whereas that for mean is the student bootstrap. However, the student bootstrap method is available for all these statistics because their standard error formulae are known as what you included. From Hesterberg, T. C. (2015). What teachers should know about the bootstrap: Resampling in the undergraduate statistics curriculum. The American Statistician, 69(4), 371–386. https://doi.org/10.1080/00031305.2015.1089789, I understand that student bootstrap confidence intervals performs best for confidence intervals of means, as illustrated in Figure 10 by bootT. But is there any comparison between bootstrap method performance on confidence intervals of variance, standard deviation, and proportion?