variance of combinations of means - off topic

You could try googling for "delta method".  I believe MASS even has code for
that...

Andy
From: Bill Shipley

Hello, and please excuse this off-topic question, but I have not been
able to find an answer elsewhere.  Consider a value Z that is 
calculated
using the product (or ratio) of two means X_mean and Y_mean:
Z=X_mean*Y_mean.  More generally, Z=f(X_mean, Y_mean).  The standard
error of Z will be a function of the standard errors of the means of X
and Y.  I want to calculate this se of Z.  Can someone direct me to a
reference (text book or other) that gives the solution to 
this *general*
problem?

Thanks.

Bill Shipley

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Hi, Andy: 

      MASS4 has section 5.7 "Bootstrap and Permutation Methods".  Is 
this what you are suggesting?  It certainly is relevant to the question 
(but not to the "delta method", except as a means of checking on it). 

      Thanks,
      spencer graves

You could try googling for "delta method".  I believe MASS even has code for
that...

Andy

From: Bill Shipley

Hello, and please excuse this off-topic question, but I have not been
able to find an answer elsewhere.  Consider a value Z that is 
calculated
using the product (or ratio) of two means X_mean and Y_mean:
Z=X_mean*Y_mean.  More generally, Z=f(X_mean, Y_mean).  The standard
error of Z will be a function of the standard errors of the means of X
and Y.  I want to calculate this se of Z.  Can someone direct me to a
reference (text book or other) that gives the solution to 
this *general*
problem?

Thanks.

Bill Shipley

[[alternative HTML version deleted]]

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You could try googling for "delta method".  I believe MASS even has code for
that...

Andy

If you have the original data you can bootstrap --- else you need the 
standar errors and
correlation between the means, and can use the delta methos as above. 
You could even
use D or deriv or deriv3 to get the derivatives automatically.

We learnt this (the delta method) in physics class in high school, to be 
able to write
the lab reports.

Kjetil
From: Bill Shipley

Hello, and please excuse this off-topic question, but I have not been
able to find an answer elsewhere.  Consider a value Z that is 
calculated
using the product (or ratio) of two means X_mean and Y_mean:
Z=X_mean*Y_mean.  More generally, Z=f(X_mean, Y_mean).  The standard
error of Z will be a function of the standard errors of the means of X
and Y.  I want to calculate this se of Z.  Can someone direct me to a
reference (text book or other) that gives the solution to 
this *general*
problem?

Thanks.

Bill Shipley

[[alternative HTML version deleted]]

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-- 

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
               --  Mahdi Elmandjra
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You could try googling for "delta method".  I believe MASS even has code for
that...

Andy

also,

help.search("delta")
does give nothing usefull, so if it is in MASS it would be hidden, and 
need a \concept
entry in the .Rd file.

The delta method is really nothimg more (or less) than a linear
Taylor approximation.

The following is a very fast implementation, which surely can be bettered:

se.delta <- function(expr, namevec, theta, sigma) {
    # theta is means, or more generally, estimates,
    # sigma is vector or matrix containing (standard errors)^2 and (if 
matrix)
    # covariances. If vector must be same length as theta, and we assume no
    # correlation between estimates theta.
    # expr must be a formula defining a function
    # taking as many arguments as length of theta.
    # namevec is a character vector containing the symbols used in the 
formula.
    p <- length(theta)
    if (!is.matrix(sigma)) sigma <- diag(sigma)
    if(!(NROW(sigma)==p)) stop("sigma and theta must have appropiate 
dimension")
    fun <- deriv(expr, namevec, TRUE)
    derivs <- do.call("fun", as.list(theta))
    derivs <- as.vector(attr(derivs, "gradient"))
    vartheta <- derivs %*% sigma %*% derivs
    setheta <- sqrt(vartheta)
    setheta
}

example:

se.delta(~ x^2 + y^2, c("x", "y"), c(0.5, 1), c(0.001, 0.001))
           [,1]
[1,] 0.07071068

(there must be possible to calculate the namevec argument from the 
formula argument, but I have no time
for that now)

Kjetil
From: Bill Shipley

Hello, and please excuse this off-topic question, but I have not been
able to find an answer elsewhere.  Consider a value Z that is 
calculated
using the product (or ratio) of two means X_mean and Y_mean:
Z=X_mean*Y_mean.  More generally, Z=f(X_mean, Y_mean).  The standard
error of Z will be a function of the standard errors of the means of X
and Y.  I want to calculate this se of Z.  Can someone direct me to a
reference (text book or other) that gives the solution to 
this *general*
problem?

Thanks.

Bill Shipley

[[alternative HTML version deleted]]

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
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http://www.R-project.org/posting-guide.html

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
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-- 

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
               --  Mahdi Elmandjra
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Checked by AVG Anti-Virus.

Liaw, Andy wrote:

You could try googling for "delta method".  I believe MASS even has code 
for
that...
I believe you are thinking of an example in S Programming, which does 
automatic differentiation and the delta method.

 	-thomas
Of course, the delta method is terrible when the first derivative 
is small relative to the curvature.  In that case, you either need to 
consider bootstrap, Monte Carlo, permutation testing, as suggested by 
Venables and Ripley in MASS and S Programming, or possibly using a 
higher order Taylor series expansion. 

      spencer graves

On Wed, 5 Jan 2005, Kjetil Brinchmann Halvorsen wrote:

Liaw, Andy wrote:

You could try googling for "delta method".  I believe MASS even has 
code for
that...

I believe you are thinking of an example in S Programming, which does 
automatic differentiation and the delta method.

    -thomas

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