How to change bootci sample size (bootstrap confidence interval)?

I'd like to adapt MATLAB's bootci function to perform resampling with a specified size.

Currently, I've implemented a basic resampling method with a fixed sample size (sizeBoot).

Here's the (slow) code snippet:

% Create random data from a normal distribution  
% with mean 28.25 and sd 8.5.  
data = (randn(1,100000)*8.5 + 28.25)'; 

nBoot = 2000; % Number of bootstraps
sizeBoot = 500; % Resampling size (bootci default is size(data))
 
bootMeans = nan(1, nBoot); 
for i = 1:Boot_number
    bootMeans(i) = mean(data(randi(numel(data), sizeBoot)));
end

% Bootci (fast)
[bci,bmeans] = bootci(nBoot,{@mean,data},'alpha',.1,'type','per'); %90 confidence interval

I believe the solution involves modifying MATLAB's bootci and bootstrp functions.

However, this task exceeds my current capabilities. Could you provide any guidance or ideas on how to achieve this modification effectively (while keeping the confidence interval types and parallel options)?

[Adam Danz]

The bootstrapped confidence interval proceedure is to resample from the entire dataset with replacement so that each sample is the same size as the data. Bootstrapping using subsampling is non-standard so the results are open to interpretation. Nevertheless, your for-loop is achieving that. Why do you need the bootci function for this?

[Ricardo]

Hello, thank you for your response.

I'm currently working on replicating some studies that utilize this method in a two-step bootstrap approach.

In the first step, I'm calculating financial return series and in the second step, I'm performing confidence interval (CI) calculations following Politis and Romano’s subsampling bootstrap.

So based on my intuition, I think that this approach is intended to improve efficiency?

Given this, I've presumed that using bootci would be the more efficient choice, especially if I can calculate the percentile ('perc') and bias-corrected and accelerated ('bca') CI methods alongside its parallel computing capabilities while reducing the sample size.

https://www.stat.umn.edu/geyer/5601/notes/sub.pdf

https://www.tandfonline.com/doi/abs/10.1080/1351847X.2015.1029590

[Adam Danz]

Thanks for the refences @Ricardo.

The percentile CIs can be computed from the bootMeans created in your for-loop.

data = (randn(100000,1)*8.5 + 28.25);
nBoot = 2000; % Number of bootstraps
sizeBoot = 500; % Resampling size (bootci default is size(data))
alpha = 0.1; 
 
n = numel(data);
bootMeans = nan(nBoot,1); 

for i = 1:nBoot
    bootMeans(i) = mean(data(randi(n, sizeBoot, 1)));
end

interval = [alpha/2, 1 - alpha/2] * 100;
CI = prctile(bootMeans,interval)

CI = 1×2

27.6042 28.8503

A comparsion of this method vs bootci is explained here and shows that these methods are equivalent.

Here's the vectorized version.

data = (randn(100000,1)*8.5 + 28.25);
nBoot = 2000; % Number of bootstraps
sizeBoot = 500; % Resampling size (bootci default is size(data))
alpha = 0.1; 
 
n = numel(data);
bootMeans = mean(data(randi(n, sizeBoot, nBoot)));

interval = [alpha/2, 1 - alpha/2] * 100;
CI = prctile(bootMeans,interval)

CI = 1×2

27.6381 28.8684