R help - Nov 2014 - Bootstrap CIs for weighted means of paired differences

Hi,

I am trying to compute bootstrap confidence intervals for weighted means of
paired differences with the boot package. Unfortunately, the weighted mean
estimate lies out of the confidence bounds and hence I am obviously doing
something wrong.

Appreciate any help. Thanks. Here is a reproducible example:


library(boot)
set.seed(1111)
x <- rnorm(50)
y <- rnorm(50)
weights <- runif(50)
weights <- weights / sum(weights)
dataset <- cbind(x,y,weights)
vw_m_diff <- function(dataset,w, d) {
    differences <- dataset[d,1]-dataset[d,2]
    weights <- w[d]
    return(weighted.mean(x=differences, w=weights))
}
res_boot <- boot(dataset, statistic=vw_m_diff, R = 1000, w=dataset[,3])
boot.ci(res_boot)

*BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS*
*Based on 1000 bootstrap replicates*

*CALL : *
*boot.ci <http://boot.ci>(boot.out = res_boot)*

*Intervals : *
*Level      Normal              Basic         *
*95%   (-0.8365, -0.3463 )   (-0.8311, -0.3441 )  *

*Level     Percentile            BCa          *
*95%   (-0.3276,  0.1594 )   (-0.4781, -0.3477 )  *

weighted.mean(x=dataset[,1]-dataset[,2], w=dataset[,3])

*[1] -0.07321734*

	[[alternative HTML version deleted]]

On Nov 14, 2014, at 12:15 PM, ivan wrote:
> Hi,
> 
> I am trying to compute bootstrap confidence intervals for weighted means of
> paired differences with the boot package. Unfortunately, the weighted mean
> estimate lies out of the confidence bounds and hence I am obviously doing
> something wrong.
> 
> Appreciate any help. Thanks. Here is a reproducible example:
> 
> 
> library(boot)
> set.seed(1111)
> x <- rnorm(50)
> y <- rnorm(50)
> weights <- runif(50)
> weights <- weights / sum(weights)
> dataset <- cbind(x,y,weights)
> vw_m_diff <- function(dataset,w, d) {
My understanding of the principle underlying the design of the bootstrapped
function was that the data was the first argument and the index vector was the
second. (I admit to not knowing what it would do with a third argument. So I
would have guessed that you wanted:

 vw_m_diff <- function(dataset,w) {
     differences <- dataset[d,1]-dataset[d,2]
    weights <- dataset[w, "weights"]
    return(weighted.mean(x=differences, w=weights))
  } 

I get what appears to me as a sensible set of estimates (since they seem
centered on zero) although I further admit I do not know what the theoretic CI
_should_ be for this problem:
> res_boot <- boot(dataset, statistic=vw_m_diff, R = 1000, w=dataset[,3])
> boot.ci(res_boot)
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 1000 bootstrap replicates

CALL : 
boot.ci(boot.out = res_boot)

Intervals : 
Level      Normal              Basic         
95%   (-0.5657,  0.4962 )   (-0.5713,  0.5062 )  

Level     Percentile            BCa          
95%   (-0.6527,  0.4249 )   (-0.5579,  0.5023 )  
Calculations and Intervals on Original Scale

>    differences <- dataset[d,1]-dataset[d,2]
>    weights <- w[d]
>    return(weighted.mean(x=differences, w=weights))
> }
> res_boot <- boot(dataset, statistic=vw_m_diff, R = 1000, w=dataset[,3])
> boot.ci(res_boot)
> 
> *BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS*
> *Based on 1000 bootstrap replicates*
> 
> *CALL : *
> *boot.ci <http://boot.ci>(boot.out = res_boot)*
> 
> *Intervals : *
> *Level      Normal              Basic         *
> *95%   (-0.8365, -0.3463 )   (-0.8311, -0.3441 )  *
> 
> *Level     Percentile            BCa          *
> *95%   (-0.3276,  0.1594 )   (-0.4781, -0.3477 )  *
> 
> weighted.mean(x=dataset[,1]-dataset[,2], w=dataset[,3])
> 
> *[1] -0.07321734*
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA