[R] variance of combinations of means - off topic

[Kjetil Brinchmann Halvorsen]

Liaw, Andy wrote:

>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]]
>>
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>>
>>    
>>
>
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>
>  
>


-- 

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
               --  Mahdi Elmandjra




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