How to find bootstrap confidence interval

bootstrap confidence interval:

Assume that the overall distribution F is unknown, but there is a data sample from the distribution F with a capacity of n, since This sample extracts a sample with a capacity of n according to the method of sampling with replacement. This sample is called a bootstrap sample. Successively and independently extract many bootstrap samples from the original sample, and use these samples to make statistical inferences about the population F. This method is called the non-parametric bootstrap method, also known as the bootstrap method.

Using the bootstrap method, the confidence interval of the variable (parameter) can be obtained, which is called the bootstrap confidence interval.

bootstrap confidence interval:

Use Python to calculate the bootstrap confidence interval:

Here is one-dimensional data as an example, sampling This mean serves as the sample estimator. The code is as follows:

import numpy as np


def average(data):
    return sum(data) / len(data)


def bootstrap(data, B, c, func):
    """
    计算bootstrap置信区间
    :param data: array 保存样本数据
    :param B: 抽样次数 通常B>=1000
    :param c: 置信水平
    :param func: 样本估计量
    :return: bootstrap置信区间上下限
    """
    array = np.array(data)
    n = len(array)
    sample_result_arr = []
    for i in range(B):
        index_arr = np.random.randint(0, n, size=n)
        data_sample = array[index_arr]
        sample_result = func(data_sample)
        sample_result_arr.append(sample_result)

    a = 1 - c
    k1 = int(B * a / 2)
    k2 = int(B * (1 - a / 2))
    auc_sample_arr_sorted = sorted(sample_result_arr)
    lower = auc_sample_arr_sorted[k1]
    higher = auc_sample_arr_sorted[k2]

    return lower, higher


if __name__ == '__main__':
    result = bootstrap(np.random.randint(0, 50, 50), 1000, 0.95, average)
    print(result)

Output:

(20.48, 28.32)

Recommended: bootstrap entry tutorial

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