R: bootstrap 是指不在 95% CI 内？

Question

library(boot)
set.seed(3)
run2 <- structure(list(X = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), 
    beta1 = c(1.40597500087168, 1.41848914211916, 1.42962301367006, 
    1.42029917323066, 1.4289966153492, 1.42596562840805, 1.42680678397731, 
    1.41425063435813, 1.40927087463386, 1.41364428128251)), .Names = c("X", 
"beta1"), class = "data.frame", row.names = 11:20)

#my boostrap mean
> b11 = mean(sample(run2$beta1, 10000, replace = TRUE)); b11
[1] 1.419424


boot.beta1 <- function(d, i){
  d2 <- d[i, ]
  return(d2$beta1)
}

> bootbeta1 <- boot(run2, boot.beta1, R = 10000)
> boot.ci(bootbeta1, type  = c("norm"))
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 10000 bootstrap replicates

CALL : 
boot.ci(boot.out = bootbeta1, type = c("norm"))

Intervals : 
Level      Normal        
95%   ( 1.377,  1.408 )  
Calculations and Intervals on Original Scale

我的 boostrapped 平均值是 1.419，但超出了 95% CI？我该如何解决这个问题？

Answer 1

bootbeta1 只是返回值的向量，而不是平均值，并且您的非 boot 版本实际上并不是引导程序，因为它没有创建用于计算统计数据的副本，而只是大量采样。

在基础 R 中，它看起来像

run2 <- data.frame(
    X = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), 
    beta1 = c(1.40597500087168, 1.41848914211916, 1.42962301367006, 1.42029917323066, 1.4289966153492, 1.42596562840805, 1.42680678397731, 1.41425063435813, 1.40927087463386, 1.41364428128251)
)

set.seed(3)
straps <- replicate(10000, mean(sample(run2$beta1, nrow(run2), replace = TRUE)))

mean(straps)
#> [1] 1.419342

# 95% confidence interval
qnorm(c(.025, .975), mean(straps), sd(straps))
#> [1] 1.414387 1.424298

boot 看起来像

library(boot)

boot_mean <- boot(run2, function(d, i){mean(d[i, 'beta1'])}, R = 10000)
boot_mean
#> 
#> ORDINARY NONPARAMETRIC BOOTSTRAP
#> 
#> 
#> Call:
#> boot(data = run2, statistic = function(d, i) {
#>     mean(d[i, "beta1"])
#> }, R = 10000)
#> 
#> 
#> Bootstrap Statistics :
#>     original        bias    std. error
#> t1* 1.419332 -1.286626e-05 0.002550844

boot_ci <- boot.ci(boot_mean, type = 'norm')
boot_ci
#> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
#> Based on 10000 bootstrap replicates
#> 
#> CALL : 
#> boot.ci(boot.out = boot_mean, type = "norm")
#> 
#> Intervals : 
#> Level      Normal        
#> 95%   ( 1.414,  1.424 )  
#> Calculations and Intervals on Original Scale

两者现在都包含平均值。

R: bootstrap 是指不在 95% CI 内？

R: bootstrap mean not inside 95% CI?

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