Bootstrap 通过 boot.ci 函数的多个统计的置信区间

Question

我想通过 boot.ci 函数获得多个统计数据的 bootstrap 置信区间。这是我的 MWE。

我在 out 中有两个统计数据，想要找到这两个统计数据的 bootstrap 置信区间。但是，boot.ci 函数仅为第一个统计数据 (t1*) 提供 bootstrap 置信区间，而不为第二个统计数据 (t2*) 提供 bootstrap 置信区间。

set.seed(12345)
df <- rnorm(n=10, mean = 0, sd = 1)


Boot.fun <- 
  function(data, idx) {
    data1 <- sample(data[idx], replace=TRUE)
    m1 <- mean(data1)
    sd1 <- sd(data1)
    out <- cbind(m1, sd1)
    return(out)
  }

Boot.fun(data = df)

library(boot)
boot.out <- boot(df, Boot.fun, R = 20)
boot.out

RDINARY NONPARAMETRIC BOOTSTRAP


Call:
  boot(data = df, statistic = Boot.fun, R = 20)


Bootstrap Statistics :
  original     bias    std. error
t1* -0.4815861  0.3190424   0.2309631
t2*  0.9189246 -0.1998455   0.2499412

boot.ci(boot.out=boot.out, conf = 0.95, type = c("norm", "basic", "perc", "bca"))

BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 20 bootstrap replicates

CALL : 
  boot.ci(boot.out = boot.out, conf = 0.95, type = c("norm", "basic", 
                                                     "perc", "bca"))

Intervals : 
  Level      Normal              Basic         
95%   (-1.2533, -0.3479 )   (-1.1547, -0.4790 )  

Level     Percentile            BCa          
95%   (-0.4842,  0.1916 )   (-0.4842, -0.4629 )  
Calculations and Intervals on Original Scale
Warning : Basic Intervals used Extreme Quantiles
Some basic intervals may be unstable
Warning : Percentile Intervals used Extreme Quantiles
Some percentile intervals may be unstable
Warning : BCa Intervals used Extreme Quantiles
Some BCa intervals may be unstable
Warning messages:
  1: In norm.inter(t, (1 + c(conf, -conf))/2) :
  extreme order statistics used as endpoints
2: In norm.inter(t, alpha) : extreme order statistics used as endpoints
3: In norm.inter(t, adj.alpha) :
  extreme order statistics used as endpoints

Answer 1

boot 软件包 (IMO) 对于常规使用来说有点笨重。简短的回答是您需要将 index（默认值为 1）指定为 boot.ci，例如boot.ci(boot.out,index=2)。长话短说，一次获得所有 bootstrap 统计数据的 bootstrap CI 肯定会很方便！

获取指定结果槽的所有 CI：

getCI <- function(x,w) {
   b1 <- boot.ci(x,index=w)
   ## extract info for all CI types
   tab <- t(sapply(b1[-(1:3)],function(x) tail(c(x),2)))
   ## combine with metadata: CI method, index
   tab <- cbind(w,rownames(tab),as.data.frame(tab))
   colnames(tab) <- c("index","method","lwr","upr")
   tab
}
## do it for both parameters
do.call(rbind,lapply(1:2,getCI,x=boot.out))

结果（可能不是你想要的，但很容易重塑）：

         index  method        lwr        upr
normal       1  normal -1.2533079 -0.3479490
basic        1   basic -1.1547310 -0.4789996
percent      1 percent -0.4841726  0.1915588
bca          1     bca -0.4841726 -0.4628899
normal1      2  normal  0.6288945  1.6086459
basic1       2   basic  0.5727462  1.4789105
percent1     2 percent  0.3589388  1.2651031
bca1         2     bca  0.6819394  1.2651031

或者，如果您可以忍受一次获得一个 bootstrap 方法，我在 Github 上的 broom 包版本具有此功能（我已经提交了一个 pull请求）

## devtools::install_github("bbolker/broom")
library(broom)
tidy(boot.out,conf.int=TRUE,conf.method="perc")

Bootstrap 通过 boot.ci 函数的多个统计的置信区间

Bootstrap Confidence Intervals for more than one statistics through boot.ci function

r

statistics-bootstrap