Bootstrap confidence intervals

This module implements the non-parametric bootstrap confidence intervals described in 'Bootstrap Confidence Intervals' by T. DiCiccio and B. Efron.

Installation

Package is available on PyPI and can be installed using pip:
pip install bootstrap-interval

Files description

• bootstrap_interval.py contains the package source code
• code.py is an example of package usage

Usage

The Boostrap class contains the resampling distribution for a given statistics

class bootstrap_interval.Bootstrap(sample, stat='mean', n_iter=10000, sample_size=None)

Parameters:
sample: data sample
stat: statistics to estimate. Can be either 'mean', 'std' or any function callable on sample
n_iter: number of resamples to use
sample_size: size of resamples. If None, equals to the size of sample
Attributes:
computed: flag if the resampling distribution was already computed
distribution: distribution of the statistics on bootstrap resamples

Methods: get_distribution(): returns the resampling distribution
get_confidence_interval(alpha, method='percentile'): returns the pair (left, right), left and right endpoints of confidence interval

get_confidence_interval(alpha, method) Arguments:
alpha: significance level, so that 1-alpha is the confidence level
method: one of 'percentile', 'sampling', 'bias_corrected': method to construct the confidence interval
if method="sampling" then confidence interval of the bootstrap distribution is used
if method="percentile" then the percentile method is used (Ch. 23.1 of van der Vaart)
if method="bias_corrected" then the bias corrected method with acceleration is used (formula 2.3 of DiCiccio and Efron)

Example

code.py contains the following simulation: A 1000 samples of length 100 are drawn from uniform distribution U(0,1). For each of the samples compute a 95%-confidence interval for the standard deviation using each of 3 methods:

for i in range(1000):
    sample = np.random.uniform(size=10**2)
    bs = bootstrap_interval.Bootstrap(sample, stat='std')
    left_bc, right_bc = bs.get_confidence_interval(0.05, method='bias_corrected')
    left_perc, right_perc = bs.get_confidence_interval(0.05, method='percentile')
    left_sampling, right_sampling = bs.get_confidence_interval(0.05, method='sampling')

Then we compute how many intervals contain the true staandard deviation value: sqrt(1/12)
bias_corrected method: 944
percentile method: 940
sampling method: 938
sizes of the confidence intervals: So the three methods show pretty close results

References:

• A. van der Vaart. Asymptotic statistics, 1998
• T. DiCiccio, B. Efron. Bootstrap Confidence Intervals. Statistical Science 1996, Vol. 11, No. 3, 189–228