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) [英] adjusted bootstrap confidence intervals (BCa) with parametric bootstrap in boot package

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:

...您是正确的，问题是您正在执行 参数引导程序.引导中实现的bca间隔为 非参数间隔，这应该已经说明 明确地在某个地方.参数bca间隔的公式 是不一样的，取决于最不利的派生 像您一样有干扰参数时的家庭可能性 案子. (请参见Davison& Hinkley的206-207页)empinf假定 统计信息是用于非参数引导的一种形式 (您在示例中对empinf的调用中做了此操作)，但是原始的 引导启动(正确)具有不同形式的统计信息 适用于参数重采样.

... you are correct that the issue is that you are doing a parametric bootstrap. The bca intervals implemented in boot are non-parametric intervals and this should have been stated explicitely somewhere. The formulae for parametric bca intervals are not the same and depend on derivatives of the least favourable family likelihood when there are nuisance parameters as in your case. (See pp 206-207 in Davison & Hinkley) empinf assumes that the statistic is in one of forms used for non-parametric bootstrapping (which you did in your example call to empinf) but your original call to boot (correctly) had the statistic in a different form appropriate for parametric resampling.

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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