如何在R中用boot()函数对male.wt数据集执行Bootstrap抽样并估计方差？

以下是使用R语言boot包完成Bootstrap抽样估计的完整步骤：

1. 安装并加载boot包 #

如果还未安装boot包，先执行安装命令：

install.packages("boot")

加载包：

library(boot)

2. 导入数据集 #

将你提供的数据集加载到R中：

malewt = structure(list(x = c(184.291514203183, 238.183299307855, 217.544606414151, 
233.931926116624, 229.12042611005, 243.881689583996, 259.230802242781, 
217.939619221934, 137.636923032685, 170.379447345948, 195.852641733122, 
185.832690963969, 186.676714564328, 215.711426139253, 186.413495533494, 
237.83223009147, 180.124153998503, 215.393108191779, 188.846039074142, 
142.373198101437, 233.234630310378, 186.141325709762, 220.062112044187, 
213.851199681057, 148.622198219149, 197.438771523918, 206.920961557603, 
190.874857845699, 217.889075914836, 152.318099234166, 218.089620221194, 
196.736930479919, 235.122424359223, 217.446826955801, 201.352404389309, 
216.290374765672, 173.85609629461, 215.961826427613, 213.87732008193, 
177.952521505061, 132.734879010504, 221.707886490889, 224.336488758995, 
218.604034088911, 228.157844234374, 196.544661577149, 228.787736646279, 
237.009125179319, 194.73342863066, 190.569523115323, 192.198491573128, 
204.589742888237, 198.662802876867, 195.238634847898, 201.834508205684, 
220.989134791548, 180.006492709174, 168.199898332071, 250.705048451896, 
209.824701073225, 212.36145906497, 205.250728119598, 196.572466206237, 
186.818746613236, 138.493748904934, 193.572713536688, 171.605082170236, 
243.803356964054, 188.768040728907, 201.408088256783, 196.23847341016, 
202.686141019735, 167.25735383257, 171.907526464761, 224.396425425799, 
183.494470842407, 220.15969728649, 143.164453849305, 152.539942653094, 
198.52004650272, 185.145815429412, 206.741840856439, 259.866591064748, 
135.212011256414, 164.2297511973, 200.623731663392, 199.599177980586, 
175.970651370212, 197.304554981825, 189.116019204125, 198.630618004183, 
185.096675814379, 203.780160863916, 174.584831373708, 150.483001599829, 
223.78078870159, 170.772181294322, 218.770812392057, 151.645084212409, 
210.350813872005)), class = "data.frame", row.names = c(NA, -100L
))

3. 定义Bootstrap统计函数 #

编写一个函数，输入原始数据和抽样索引，返回该样本的方差：

var_bootstrap <- function(data, indices) {
  # 从原始数据中按索引抽取Bootstrap样本
  sample_data <- data$x[indices]
  # 计算样本方差
  var(sample_data)
}

4. 执行Bootstrap抽样 #

调用boot()函数，指定数据集、统计函数和抽样次数（这里用10000次，次数越多结果越稳定）：

boot_result <- boot(data = malewt, statistic = var_bootstrap, R = 10000)

5. 查看结果 #

打印Bootstrap结果：

print(boot_result)

输出包含：

• t0：原始样本的方差
• t：10000次Bootstrap样本的方差集合
• 标准差估计等信息

获取Bootstrap估计值和置信区间 #

计算所有Bootstrap样本方差的均值，作为总体方差的Bootstrap估计：

mean(boot_result$t)

生成95%置信区间：

boot.ci(boot_result, type = c("norm", "basic", "perc"))

这里提供三种常见的置信区间类型：正态近似、基础Bootstrap、百分位数法，可按需选择。

结果解释 #

• Bootstrap估计值：多次抽样得到的方差平均值，是总体方差的无偏估计
• 置信区间：表示我们有95%的把握认为总体方差落在该区间内

内容的提问来源于stack exchange，提问作者Simon