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# Re: st: re: Cumulative Accuracy Profile

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: re: Cumulative Accuracy Profile Date Thu, 3 Feb 2011 09:18:45 +0000

```The name for the common fruit fly is Drosophila [not ...philia]
melanogaster. Genus names are capitalised, specific names are not.

In terms of the question, if you are minimising RMSE you are also
minimising its square. In other words, this problem is nonlinear
linear squares and there is absolutely no need to program it yourself.
Head straight for the help and the manual entry for -nl-.

Nick

On Thu, Feb 3, 2011 at 5:52 AM, Drosophilia Melanogaster

> How does one program an algorithm that estimates the concavity of a Cumulative Accuracy Profile (CAP) curve? I wish to fit a model for y using the function:
>
> y = [1- exp(-kx)]/[1-exp(-k)]
>
> where k is my parameter of interest and is obtained by minimizing a root mean square  error (RMSE) of the form:
>
>
> e = sqrt{(1/N)*summation i to n of [y_i - [1- exp(-kx_i)]/[1-exp(-k)]]^2}.
>
>
> The RMSE is minimized by applying a Newton-Raphson procedure using the following iteration (i=1,2... 20):
>
>
> k_i+1 = k_i - [(de/dk)/(d2e/dk2)]     (ratio of derivatives)
>
>

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