Forum: help

RE: maxNM [ Reply ]
By: Ott Toomet on 2015-01-10 09:11

Unfortunately I do not. I recommend you to look at the related literature. We just canned the existing function in our package.

I see no reason why it should not work, just perhaps it is slower as it does not rely on gradients. It is easy to play with some sort of examples (estimate an OLS problem by NM optimization, for instance) and try it out. However, this method is intended to be used in situations where gradient does not work/is not available, so don't use it if you can use gradients (it is slower).

I would be happy if you can figure it out and let us know :-)

RE: maxNM [ Reply ] By: Graziella Bonanno on 2015-01-09 16:58	[forum:41780]
Thank you Ott Toomet for your answer, but I have another question. Do you know if NM works well even if the parameters to be estimated are more of two or three? Thank you very much. Best, Graziella

RE: maxNM [ Reply ]
By: Ott Toomet on 2015-01-09 05:07

[forum:41777]

I don't know myself much about Nelder-Mead method. It is a not-gradient-based method, so you can use it for non-differentiable functions, or in situations were numeric derivatives do not work. It is a wrapper to optim() function from the maxLik perspective. As a well-established optimization technique, I guess it typically works well.

A tiny example gives very similar results:
> summary(maxNM(loglikBFGS.OB, start=c(0,1)))
--------------------------------------------
Nelder-Mead maximisation
Number of iterations: 47
Return code: 0
successful convergence
Function value: -1345.375
Estimates:
estimate gradient
[1,] 0.04960003 0.03658715
[2,] 0.92909851 -0.04898243
--------------------------------------------
> summary(maxNR(loglikBFGS.OB, start=c(0,1)))
--------------------------------------------
Newton-Raphson maximisation
Number of iterations: 4
Return code: 1
gradient close to zero
Function value: -1345.375
Estimates:
estimate gradient
[1,] 0.04963161 0.000000e+00
[2,] 0.92907737 2.273737e-07
--------------------------------------------

where the objective function looks like

loglikBFGS.OB <- function(beta) {
mu <- beta[1]
sigma <- beta[2]
sum(dnorm(x, mean=mu, sd=sigma, log=TRUE))
}

So I guess you should either do some testing yourself, or read a bit about NM method. Sorry, I cannot help you much here.

maxNM [ Reply ] By: Graziella Bonanno on 2015-01-07 12:13	[forum:41774]
Dear All, I am wondering if the Nelder-Mead algorithm is reliable, or better if it provides reliable estimates and if these estimates can be considered as maximum of the function even if I do not obtain null gradient using "numericGradient" command. Thanks a lot, Graziella