How to know which distribution is BCa method form bootci assuming my data follows
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I am using th bootci function to compute the confidence interval around the mean of my dataset. I am using the line of code below
[ci,bootstat] = bootci(100000,@(x)[mean(x) std(x)],y);
where y is my dataset vector. I know that by default the function will use the BCa method to compute the 95% confidence intervals around the mean and the standard deviation of my data. My question is how can I know which distribution is the BCa method assuming the bootstrapped data set follows?
Ive J on 12 Sep 2021
To my understanding BCa tries to correct for bias and skewness (acceleration, calculated from jackknife sampling) in the distribution of estimates, and both of these corrections depend on your original sample. These corrections are then used to adjust cirtical values from norminv, and returning it's CDF. So, assuming both correction factors are zero, this is equivalent to assuming a normal distribution and intervals would be those estimated from typical bootstrap percentile interval (although may be biased).
the cyclist on 11 Sep 2021
I don't have a definitive answer, but looking inside the code of bootci.m (by using edit bootci), I see enough usage of norminv and normcdf to guess that it is assuming normal.
That being said, I did not carefully step through the code to understand it. I will say that there are more-than-usual references inside the code, to the paper DiCiccio, Thomas J., and Bradley Efron. “Bootstrap Confidence Intervals.” Statistical Science 11, no. 3 (1996): 189–228. (This reference is given in the documentation.) So, to be really confident, I think you'd need to understand that reference.