Have you tried writing a function to compute SS = sum of squares
deviations between the the left and right hand sides of your three
equations, then using 'optim'? See also Venables and Ripley (2002)
Modern Applied Statistics with S, 4th ed. (Springer).
hope this helps.
Spencer Graves
p.s. I don't see how it's obvious that 'a=-c'.
Kjetil Brinchmann Halvorsen wrote:
> HAKAN DEMIRTAS wrote:
>> I can't seem to get computationally stable estimates for the following
>> system:
>>
>> Y=a+bX+cX^2+dX^3, where X~N(0,1). (Y is expressed as a linear combination of
>> the first three powers of a standard normal variable.) Assuming that E(Y)=0
>> and Var(Y)=1, one can obtain the following equations after tedious algebraic
>> calculations:
>>
>> 1) b^2+6bd+2c^2+15d^2=1
>> 2) 2c(b^2+24bd+105d^2+2)=E(Y^3)
>> 3) 24[bd+c^2(1+b^2+28bd)+d^2(12+48bd+141c^2+225d^2)]=E(Y^4)-3
>>
>> Obviously, a=-c. Suppose that distributional form of Y is given so we know
>> E(Y^3) and E(Y^4). In other words, we have access to the third and fourth
>> raw moments. How do we solve for these four coefficients? I reduced the
>> number of unknowns/equations to two, and subsequently used a grid approach.
>> It works well when I am close to the center of the support, but fails
>> miserably at the tails. Any ideas? Hopefully, there is a nice R function
>> that does this.
>>
>> Hakan Demirtas
>>
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-devel@r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
> This is really a question for r-help not r-devel.
>
> I was about to say that this was a question for a symbolic algebra
> system, but first tried in MuPAD 4.0, and left the machine alone.
> returning after 2 hours MuPAD was still grinding and I had to kill it.
>
> Kjetil
>
> ______________________________________________
> R-devel@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
______________________________________________
R-devel@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel
