引导程序包中的参数引导程序可调整引导程序置信区间(BCa)

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问题描述

我正在尝试使用R的boot包中的boot.ci从参数引导程序计算经过偏差和偏斜校正的引导程序置信区间.通过阅读手册页和实验，我得出结论，我必须自己计算折刀估计值并将其输入boot.ci，但这在任何地方都没有明确说明.我没有找到其他文档，尽管公平地说，我没有看过基于Davison和Hinkley编写代码的原始书...

I am attempting to use boot.ci from R's boot package to calculate bias- and skew-corrected bootstrap confidence intervals from a parametric bootstrap. From my reading of the man pages and experimentation, I've concluded that I have to compute the jackknife estimates myself and feed them into boot.ci, but this isn't stated explicitly anywhere. I haven't been able to find other documentation, although to be fair I haven't looked at the original Davison and Hinkley book on which the code is based ...

如果我天真地先运行b1 <- boot(...,sim="parametric")，然后再运行boot.ci(b1)，则会收到错误influence values cannot be found from a parametric bootstrap.当且仅当我指定type="all"或type="bca"时，才会发生此错误. boot.ci(b1,type="bca")给出相同的错误. empinf(b1)也是如此.使工作正常的唯一方法是显式计算折刀估计值(将empinf()与data参数一起使用)并将其输入到boot.ci中.

If I naively run b1 <- boot(...,sim="parametric") and then boot.ci(b1), I get the error influence values cannot be found from a parametric bootstrap. This error occurs if and only if I specify type="all" or type="bca"; boot.ci(b1,type="bca") gives the same error. So does empinf(b1). The only way I can get things to work is to explicitly compute jackknife estimates (using empinf() with the data argument) and feed these into boot.ci.

构造数据:

set.seed(101)
d <- data.frame(x=1:20,y=runif(20))
m1 <- lm(y~x,data=d)

引导程序:

b1 <- boot(d$y,
           statistic=function(yb,...) {
             coef(update(m1,data=transform(d,y=yb)))
           },
           R=1000,
           ran.gen=function(d,m) {
             unlist(simulate(m))
           },
           mle=m1,
           sim="parametric")

到目前为止还不错.

boot.ci(b1)
boot.ci(b1,type="bca")
empinf(b1)

全部给出上述错误.

这有效:

L <- empinf(data=d$y,type="jack",
            stype="i",
            statistic=function(y,f) {
              coef(update(m1,data=d[f,]))
            })

boot.ci(b1,type="bca",L=L)

有人知道我是否应该这样做吗?

Does anyone know if this is the way I'm supposed to be doing it?

更新:boot软件包的原始作者回复了一封电子邮件:

update: The original author of the boot package responded to an e-mail:

您当然可以做您正在做的事情，但是我不确定混合参数重采样的理论特性非参数区间估计.

You can certainly do what you're doing but I am not sure of the theoretical properties of mixing parametric resampling with non-parametric interval estimation.

推荐答案

查看boot.ci页面后，我决定使用按照Davison和Hinkley第6章中的示例构造的启动对象，并查看是否它产生了您观察到的错误.我确实收到警告，但没有错误.

After looking at the boot.ci page I decided to use a boot-object constructed along the lines of an example in Ch 6 of Davison and Hinkley and see whether it generated the errors you observed. I do get a warning but no errors.:

require(boot) 
lmcoef <- function(data, i){
      d <- data[i, ]
      d.reg <- lm(y~x, d)
      c(coef(d.reg)) }
lmboot <- boot(d, lmcoef, R=999)
m1
boot.ci(lmboot, index=2)   # I am presuming that the interest is in the x-coefficient
#----------------------------------
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 999 bootstrap replicates

CALL : 
boot.ci(boot.out = lmboot, index = 2)

Intervals : 
Level      Normal              Basic         
95%   (-0.0210,  0.0261 )   (-0.0236,  0.0245 )  

Level     Percentile            BCa          
95%   (-0.0171,  0.0309 )   (-0.0189,  0.0278 )  
Calculations and Intervals on Original Scale
Warning message:
In boot.ci(lmboot, index = 2) :
  bootstrap variances needed for studentized intervals

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