# Uncorrelated random vectors

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## Uncorrelated random vectors

 Hello, is it possible to create two uncorrelated random vectors for a given distribution. In fact, I would like to have something like the function "rnorm" or "rlogis" with the extra property that they are uncorrelated. Thanks for your help, Luba         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Uncorrelated random vectors

 Thank you for your help! But is it possible to produe two vectors x and y with a given length such that there correlation is zero. For me ist not enough just to simulate two vectors with there correlation. Thank you, Luba -----Urspr?ngliche Nachricht----- Von: ONKELINX, Thierry [mailto:[hidden email]] Gesendet: Dienstag, 7. Juli 2009 15:51 An: Stein, Luba (AIM SE); [hidden email] Betreff: RE: [R] Uncorrelated random vectors cor.test(rnorm(10000), rnorm(10000)) ------------------------------------------------------------------------ ---- ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest Cel biometrie, methodologie en kwaliteitszorg / Section biometrics, methodology and quality assurance Gaverstraat 4 9500 Geraardsbergen Belgium tel. + 32 54/436 185 [hidden email] www.inbo.be To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data. ~ Roger Brinner The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey -----Oorspronkelijk bericht----- Van: [hidden email] [mailto:[hidden email]] Namens Stein, Luba (AIM SE) Verzonden: dinsdag 7 juli 2009 15:46 Aan: [hidden email] Onderwerp: [R] Uncorrelated random vectors Hello, is it possible to create two uncorrelated random vectors for a given distribution. In fact, I would like to have something like the function "rnorm" or "rlogis" with the extra property that they are uncorrelated. Thanks for your help, Luba         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code. Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer en binden het INBO onder geen enkel beding, zolang dit bericht niet bevestigd is door een geldig ondertekend document. The views expressed in  this message and any annex are purely those of the writer and may not be regarded as stating an official position of INBO, as long as the message is not confirmed by a duly signed document. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Uncorrelated random vectors

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## Re: Uncorrelated random vectors

 In reply to this post by Stein, Luba (AIM SE) Be careful to be clear what you are referring to when you say "correlation is zero". The commands   x <- rnorm(100)   y <- rnorm(100) will produce two vectors of given length (100) which (to within the effectively ignorable limitations of the ransom number generator) will have been produced independently. Hence the *theoretical* correlation is zero. If that is what you meant, then it is already answered. When you compute cor(x,y), however, the answer will in general be non-zero (though only rarely significantly so). This is because the numbers produced by the second independent run of rnrom() have an almost zero probability of producing two vectors for which the value of cor(x,y) = 0. However, possibly you mean that you want two vectors for which the result of cor(x,y) = 0. One way to achieve this is along the following lines:   set.seed(54321)   x  <- rnorm(100)   y0 <- rnorm(100)   My <- mean(y0)   Sy <- sd(y0)   y1 <- lm(y0 ~ x)\$res ; y1 <- y1/sd(y1)   y  <- My + y1*Sy   mean(y0)   # [1] 0.04497584   mean(y)   # [1] 0.04497584   sd(y0)   # [1] 0.848231   sd(y)   # [1] 0.848231   cor(x,y0)   # [1] 0.05556468   cor(x,y)   # [1] 6.451072e-18 [effectively 0, to within rounding error] In this case, however, note that [A]: The 100 elements of y, given the values of x, are NOT independent of each other, since they satisfy the linear constraint   x[1]*y[1] + x[2]*y[2] + ... + x[100]*y[100]       - (sum(x))*[y[1] + y[2] + ... + y[100])/100 = 0 and therefore can vary only in 99 dimensions, not 100. Nor are they independent of the values of x (even though the numerical correlation is 0). On the other hand, the values of y0 are independent of the values of x, and of each other. You need to be very clear why you want to have two vectors x,y such that cor(x,y) = 0, since otherwise you are at risk of carrying out an invalid analysis. Hoping this helps, Ted. On 07-Jul-09 14:26:02, Stein, Luba (AIM SE) wrote: > Thank you for your help! > But is it possible to produe two vectors x and y with a given length > such that there correlation is zero. > > For me ist not enough just to simulate two vectors with there > correlation. > > Thank you, > Luba > > > > > -----Urspr?ngliche Nachricht----- > Von: ONKELINX, Thierry [mailto:[hidden email]] > Gesendet: Dienstag, 7. Juli 2009 15:51 > An: Stein, Luba (AIM SE); [hidden email] > Betreff: RE: [R] Uncorrelated random vectors > > cor.test(rnorm(10000), rnorm(10000)) > > > ------------------------------------------------------------------------ > ---- > ir. Thierry Onkelinx > ~ Roger Brinner > > The combination of some data and an aching desire for an answer does > not > ensure that a reasonable answer can be extracted from a given body of > data. > ~ John Tukey > > -----Oorspronkelijk bericht----- > Van: [hidden email] [mailto:[hidden email]] > Namens Stein, Luba (AIM SE) > Verzonden: dinsdag 7 juli 2009 15:46 > Aan: [hidden email] > Onderwerp: [R] Uncorrelated random vectors > > Hello, > > is it possible to create two uncorrelated random vectors for a given > distribution. > > In fact, I would like to have something like the function "rnorm" or > "rlogis" with the extra property that they are uncorrelated. > > Thanks for your help, > Luba -------------------------------------------------------------------- E-Mail: (Ted Harding) <[hidden email]> Fax-to-email: +44 (0)870 094 0861 Date: 07-Jul-09                                       Time: 16:48:06 ------------------------------ XFMail ------------------------------ ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Uncorrelated random vectors

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## Re: Uncorrelated random vectors

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## Re: Uncorrelated random vectors

 In reply to this post by Stein, Luba (AIM SE) As mentioned by somebody before, there is no problem for the normal case - use mvrnorm function from MASS package with any mu and make Sigma be any diagonal matrix (with strictly positive diagonal). Note that even though all the correlations are 0, the SAMPLE correlations won't be 0. If you want to create a set of vectors whose SAMPLE correlations are 0 you will have to use a variant of Gramm-Schmidt. I do not know whether a variant of mvrnorm exists for logistic distribution (my guess is that it does not). --- On Tue, 7/7/09, Stein, Luba (AIM SE) <[hidden email]> wrote: > From: Stein, Luba (AIM SE) <[hidden email]> > Subject: [R] Uncorrelated random vectors > To: "[hidden email]" <[hidden email]> > Received: Tuesday, 7 July, 2009, 11:45 PM > Hello, > > is it possible to create two uncorrelated random vectors > for a given distribution. > > In fact, I would like to have something like the function > "rnorm" or "rlogis" with the extra property that they are > uncorrelated. > > Thanks for your help, > Luba > > > > >     [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] > 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. > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.