# [R] Speed up studentized confidence intervals ?

David Winsemius dw|n@em|u@ @end|ng |rom comc@@t@net
Thu Dec 30 02:22:10 CET 2021

```On 12/29/21 11:08 AM, varin sacha via R-help wrote:
> Dear David,
> Dear Rui,
>
> Many thanks for your response. It perfectly works for the mean. Now I have a problem with my R code for the median. Because I always get 1 (100%) coverage probability that is more than very strange. Indeed, considering that an interval whose lower limit is the smallest value in the sample and whose upper limit is the largest value has 1/32 + 1/32 = 1/16 probability of non-coverage, implying that the confidence of such an interval is 15/16 rather than 1 (100%), I suspect that the confidence interval I use for the median is not correctly defined for n=5 observations, and likely contains all observations in the sample ? What is wrong with my R code ?

Seems to me that doing  a bootstrap within a `replicate` call is not
needed. (Use one or the other as a mechanism for replication.

Here's what I would consider to be a "bootstrap" operation for
estimating a 95% CI on the Gamma distributed population you created:

Used a sample size of 10000 rather than 100000

> quantile( replicate( 1000, {median(sample(s,5))}) , .5+c(-0.475,0.475))
2.5%     97.5%
0.1343071 0.6848352

This is using boot::boot to calculate medians of samples of size 5

> med <- function( data, indices) {
+     d <- data[indices[1:5]] # allows boot to select sample
+     return( median(d))
+ }
> res <- boot(data=s, med, 1000)

> str(res)
List of 11
\$ t0       : num 0.275
\$ t        : num [1:1000, 1] 0.501 0.152 0.222 0.11 0.444 ...
\$ R        : num 1000
\$ data     : num [1:10000] 0.7304 0.4062 0.1901 0.0275 0.2748 ...
\$ seed     : int [1:626] 10403 431 -118115842 -603122380 -2026881868
758139796 1148648893 -1161368223 1814605964 -1456558535 ...
\$ statistic:function (data, indices)
..- attr(*, "srcref")= 'srcref' int [1:8] 1 8 4 1 8 1 1 4
.. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile'
<environment: 0x5562fcb434e8>
\$ sim      : chr "ordinary"
\$ call     : language boot(data = s, statistic = med, R = 1000)
\$ stype    : chr "i"
\$ strata   : num [1:10000] 1 1 1 1 1 1 1 1 1 1 ...
\$ weights  : num [1:10000] 1e-04 1e-04 1e-04 1e-04 1e-04 1e-04 1e-04
1e-04 1e-04 1e-04 ...
- attr(*, "class")= chr "boot"
- attr(*, "boot_type")= chr "boot"

> quantile( res\$t , .5+c(-0.475,0.475))
2.5%     97.5%
0.1283309 0.6821874

>
> ########################################
> library(boot)
>
> s=rgamma(n=100000,shape=2,rate=5)
> median(s)
>
> N <- 100
> out <- replicate(N, {
> a<- sample(s,size=5)
> median(a)
>
> dat<-data.frame(a)
> med<-function(d,i) {
> temp<-d[i,]
> median(temp)
> }
>
>    boot.out <- boot(data = dat, statistic = med, R = 10000)
>    boot.ci(boot.out, type = "bca")\$bca[, 4:5]
> })
>
> #coverage probability
> median(out[1, ] < median(s) & median(s) < out[2, ])
> ########################################
>
>
>
>
> Le jeudi 23 décembre 2021, 14:10:36 UTC+1, Rui Barradas <ruipbarradas using sapo.pt> a écrit :
>
>
>
>
>
> Hello,
>
> The code is running very slowly because you are recreating the function
> in the replicate() loop and because you are creating a data.frame also
> in the loop.
>
> And because in the bootstrap statistic function med() you are computing
> the variance of yet another loop. This is probably statistically wrong
> but like David says, without a problem description it's hard to say.
>
> Also, why compute variances if they are never used?
>
> Here is complete code executing in much less than 2:00 hours. Note that
> it passes the vector a directly to med(), not a df with just one column.
>
>
> library(boot)
>
> set.seed(2021)
> s <- sample(178:798, 100000, replace = TRUE)
> mean(s)
>
> med <- function(d, i) {
>    temp <- d[i]
>    f <- mean(temp)
>    g <- var(temp)
>    c(Mean = f, Var = g)
> }
>
> N <- 1000
> out <- replicate(N, {
>    a <- sample(s, size = 5)
>    boot.out <- boot(data = a, statistic = med, R = 10000)
>    boot.ci(boot.out, type = "stud")\$stud[, 4:5]
> })
> mean(out[1, ] < mean(s) & mean(s) < out[2, ])
> # 0.952
>
>
>
> Hope this helps,
>
>
> Às 11:45 de 19/12/21, varin sacha via R-help escreveu:
>> Dear R-experts,
>>
>> Here below my R code working but really really slowly ! I need 2 hours with my computer to finally get an answer ! Is there a way to improve my R code to speed it up ? At least to win 1 hour ;=)
>>
>> Many thanks
>>
>> ########################################################
>> library(boot)
>>
>> s<- sample(178:798, 100000, replace=TRUE)
>> mean(s)
>>
>> N <- 1000
>> out <- replicate(N, {
>> a<- sample(s,size=5)
>> mean(a)
>> dat<-data.frame(a)
>>
>> med<-function(d,i) {
>> temp<-d[i,]
>> f<-mean(temp)
>> g<-var(replicate(50,mean(sample(temp,replace=T))))
>> return(c(f,g))
>>
>> }
>>
>>      boot.out <- boot(data = dat, statistic = med, R = 10000)
>>      boot.ci(boot.out, type = "stud")\$stud[, 4:5]
>> })
>> mean(out[1,] < mean(s) & mean(s) < out[2,])
>> ########################################################
>>
>> ______________________________________________
>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
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>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.

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