[R] Bug : Autocorrelation in sample drawn from stats::rnorm

[hmh]

Hi,


I just noticed the following bug:

When we draw a random sample using the function stats::rnorm, there 
should be not auto-correlation in the sample. But their is some 
auto-correlation _when the sample that is drawn is small_.

I describe the problem using two functions:

DistributionAutocorrelation_Unexpected which as the wrong behavior : 
_when drawing some small samples using rnorm, there is generally a 
strong negative auto-correlation in the sample_.

and

DistributionAutocorrelation_Expected which illustrate the expected behavior



*Unexpected : *

DistributionAutocorrelation_Unexpected = function(SampleSize){
   Cor = NULL
   for(repetition in 1:1e5){
     X = rnorm(SampleSize)
     Cor[repetition] = cor(X[-1],X[-length(X)])
   }
   return(Cor)
}

par(mfrow=c(3,3))
for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
hist(DistributionAutocorrelation_Unexpected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_)) 
; abline(v=0,col=2)
}

output:


*Expected**:*

DistributionAutocorrelation_Expected = function(SampleSize){
   Cor = NULL
   for(repetition in 1:1e5){
     X = rnorm(SampleSize)
*    Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)]))*
   }
   return(Cor)
}

par(mfrow=c(3,3))
for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
hist(DistributionAutocorrelation_Expected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_)) 
; abline(v=0,col=2)
}




Some more information you might need:


packageDescription("stats")
Package: stats
Version: 3.5.1
Priority: base
Title: The R Stats Package
Author: R Core Team and contributors worldwide
Maintainer: R Core Team <R-core using r-project.org>
Description: R statistical functions.
License: Part of R 3.5.1
Imports: utils, grDevices, graphics
Suggests: MASS, Matrix, SuppDists, methods, stats4
NeedsCompilation: yes
Built: R 3.5.1; x86_64-pc-linux-gnu; 2018-07-03 02:12:37 UTC; unix

Thanks for correcting that.

fill free to ask any further information you would need.

cheers,

hugo


-- 
- no title specified

Hugo Mathé-Hubert

ATER

Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC)

UMR 7360 CNRS -  Bât IBISE

Université de Lorraine  -  UFR SciFA

8, Rue du Général Delestraint

F-57070 METZ

+33(0)9 77 21 66 66
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