python - 我创建了一个类来在引导后返回置信区间，但我的置信区间看起来异常狭窄。我做错了什么？

Question

我的意图是让代码对给定列表执行引导(统计)样本量等于列表长度 10,000 次，然后计算95% 置信区间。

import numpy
from random import choice

class bootstrapping(object):

    def __init__(self,bslist=[],iteration=10000):
        self.bslist = bslist
        self.iteration = iteration

    def CI(self):
        listofmeans = []

        for numbers in range(0,self.iteration):
            bootstraplist = [choice(self.bslist) for _ in range(len(self.bslist))]
            listofmeans.append(sum(bootstraplist) / len(bootstraplist))

        s = numpy.std(listofmeans)
        z = 1.96
        n = self.iteration**0.5

        lower_confidence = (sum(listofmeans) / len(listofmeans)) - (z*s/n)
        upper_confidence = (sum(listofmeans) / len(listofmeans)) + (z*s/n)

        return lower_confidence,upper_confidence

test = bootstrapping([60,33,102,53,63,33,42,19,31,86,15,50,
                      45,47,26,23,30,20,18,48,22,20,17,29,43,52,29],10000)
test.CI()

我得到的置信区间 (37.897427638499948, 38.102572361500052) 是奇怪的狭窄。当我将相同的数字列表输入 Minitab 时，95%我得到的置信区间是 (30.74, 47.48)。我做错了什么吗？

Answer 1

要找到 95% 的置信区间，让 z = 1.96(近似值)并计算平均值的区间，加上或减去 z*std 其中 std 是标准偏差。换句话说，使用 z*std 而不是 z*std/n:

import numpy as np
import random
random.seed(2017)

class Bootstrapping(object):

    def __init__(self,bslist=[],iteration=10000):
        self.bslist = bslist
        self.iteration = iteration

    def CI(self):
        listofmeans = []

        for numbers in range(0,self.iteration):
            bootstraplist = [random.choice(self.bslist) for _ in range(len(self.bslist))]
            mean = sum(bootstraplist) / len(bootstraplist)
            listofmeans.append(mean)

        mean = np.mean(listofmeans, axis=0)
        std = np.std(listofmeans, axis=0)
        z = 1.96
        err = z*std
        lower_confidence = mean - err
        upper_confidence = mean + err

        return lower_confidence, upper_confidence

test = Bootstrapping([60,33,102,53,63,33,42,19,31,86,15,50,
                      45,47,26,23,30,20,18,48,22,20,17,29,43,52,29],10000)
print(test.CI())

产量

(31.309540089458281, 46.876348799430602)

---

或者，您可以计算置信区间而不求助于均值 +/-1.96*std 公式。您可以通过对 listofmeans 进行排序并找到第 5 个和第 95 个百分位数的值来获得置信区间的经验估计值:

import random
random.seed(2017)

class Bootstrapping(object):

    def __init__(self,bslist=[],iteration=10000):
        self.bslist = bslist
        self.iteration = iteration

    def CI(self):
        listofmeans = []

        for numbers in range(0,self.iteration):
            bootstraplist = [random.choice(self.bslist) for _ in range(len(self.bslist))]
            mean = sum(bootstraplist) / len(bootstraplist)
            listofmeans.append(mean)

        listofmeans = sorted(listofmeans)    
        a, b = round(self.iteration*0.05), round(self.iteration*0.95)
        lower_confidence = listofmeans[a]
        upper_confidence = listofmeans[b]

        return lower_confidence, upper_confidence

test = Bootstrapping([60,33,102,53,63,33,42,19,31,86,15,50,
                      45,47,26,23,30,20,18,48,22,20,17,29,43,52,29],10000)
print(test.CI())

产量

(32.888888888888886, 45.888888888888886)