[R] error propagation - hope it is correct subject

[Petr Pikal]

Hallo Thomas

Thank you for your answer, even I am not sure how to do it in R (or maybe at 
all). My mathematics background is only faint so I drop the first possibility which 
is for me rather cryptic. 

Does your second suggestion mean:

1:	compute random variable  y <- f(rnorm(n,mymeanx1,mysdx1), 
rnorm(n,mymeanx2, ...), ...)

according to my function f  (based on assumption x variables values can be 
considered normally distributed and and independent)

2:	sd(y)

can be considered as variation of y?
Or is it necessary to do something like

vysled<-NULL
for (i in 1:300) vysled[i]<-sd(sample(y,100))
mean(vysled)

to get bootstraped estimation of sd(y)

My actual data have some missing values and some outliers which I can either 
remove or to use some robust statistics for mean and variation estimates.

Thank you and have a nice Christmas

Petr

On 22 Dec 2003 at 8:56, Thomas W Blackwell wrote:

> Petr  -
> 
> Very briefly, I think of three ways to approximate the standard
> deviation of  y = f(x1,x2,x3).
> 
>   (1) linearise f() and use the covariance matrix of [x1,x2,x3].
>   (2) simulate draws from the joint distribution of [x1,x2,x3],
>  then compute the sample std dev of resulting f()s.
>   (3) go back to the original data set from which [x1,x2,x3] were
>  estimated as parameters, re-sample rows with replacement,
>  estimate [x1,x2,x3] and compute f, then take sample std dev.
> 
> Other names for these three would be (1) the "delta method" or
> Taylor series expansion, (2) parametric bootstrap, (3) bootstrap.
> 
> Different choices are appropriate in different situations.
> 
> If the std devs of x1,x2,x3 are small relative to the curvature
> (2nd derivative) in f(), then use (1) and compute by matrix algebra
> 
> Var(f(x1,x2,x3))  approx  t(grad f) %*% Cov(x1,x2,x3) %*% grad f.
> 
> If the curvature in f() is an issue, use (2) with draws of x1,x2,x3
> from some parametric distribution (eg, rnorm()) with each component
> properly conditioned on the ones already drawn.
> 
> Only if there were no set of intermediate parameters [x1,x2,x3]
> would I use (3) to get the precision of f directly.  I'm sure
> Brad Efron would say something different.  (3) is the only one
> that is canned in R, simply because the other two are practically
> one-liners.
> 
> -  tom blackwell  -  u michigan medical school  -  ann arbor  -
> 
> On Mon, 22 Dec 2003, Petr Pikal wrote:
> 
> > Dear all
> >
> > Please, can you advice me how to compute an error, standard
> > deviation or another measure of variability of computed value.
> >
> > I would like to do something like:
> >
> > var(y) = some.function(var(x1),var(x2),var(x3))
> >
> > for level F1 (2,3,...)
> >
> > Let say I have some variables - x1, x2, x3 (two computed for levels
> > of factor F and one which is same for all levels) and I want to
> > compute
> >
> > y = f(x1,x2,x3)
> >
> > for some levels of factor F
> >
> > I can compute variation of variables for levels of F, I know a
> > variation of one variable but I am not sure how to transfer it to
> > variation of y within respective levels.
> >
> > I found some methods which I can use but I wonder if  there is some
> > method implemented in R (Manly B.F. Biom.J.28,949,(1986), some local
> > statistical books available to me).
> >
> > I have a feeling I could use bootstrap method for this but I am not
> > sure how.
> >
> > Thank you and merry Christmas to all
> >
> > Petr Pikal
> > petr.pikal at precheza.cz
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> >
> 
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Petr Pikal
petr.pikal at precheza.cz