R help - Jan 2011 - Weighted Optimization

Hi All,

I am trying to code an R script which gives me the time varying parameters of
the NIG and GH distributions. Further, becasue I think these these time varying
parameters should be more responsive to more recent observations, I would like
to include a weighted likelihood estimation proceedure where the observations
have an exponentially decaying weighting rather than the equal weighting implied
by a standard MLE approach.

The optimization function which leads to my parameter estimates is given by;

gh.fit = try(optim(vega, negllh,hessian = se,pdf = gh.pdf,
         tmp.data = data, transf = transform, const.pars = vars[!opt.pars],
         silent = silent, par.names = names(vars), ...))

param.est = gh.fit$par

In the above, vega are the parameters to estimate and pdf is the GH pdf. This
seems to work well for the case where observations are equally weighted.
However, I'm stuck on how to include a weighted vector (w_i) to turn this
problem into a weighted ML optimization.

Would you please be able to suggest a function or change in code which may allow
me to do this?

Thank you in advance for your time.

Jason

You will have to modify your likelihood in such a way that it also  
includes the weights. If your likelihood has the following form: l =  
sum(log p_i) you could for example add the weights to the likelihood:  
lw = sum(w_i * log p_i) (although I am not sure that this is the  
correct way to add the weights in your case)

Therefore, you will have to change your functions negllh and se to
also accepts the weights as input parameters:

negllh <- function([PARAMETERS YOU HAVE ALREADY HERE], weights, ...) }{ ... }
se <- function([PARAMETERS YOU HAVE ALREADY HERE], weights, ...) { ... }

You can then call optim adding weights as additional parameter which
gets passed on to negllh and se:

gh.fit = try(optim(vega, negllh,hessian = se,pdf = gh.pdf,
           tmp.data = data, transf = transform, const.pars = vars[!opt.pars],
           silent = silent, par.names = names(vars), weights = w, ...))

HTH,

Jan



Quoting JASON SCALLY <j.scally at student.qut.edu.au>:
> Hi All,
>
> I am trying to code an R script which gives me the time varying    
> parameters of the NIG and GH distributions. Further, becasue I think  
>   these these time varying parameters should be more responsive to    
> more recent observations, I would like to include a weighted    
> likelihood estimation proceedure where the observations have an    
> exponentially decaying weighting rather than the equal weighting    
> implied by a standard MLE approach.
>
> The optimization function which leads to my parameter estimates is given
by;
>
> gh.fit = try(optim(vega, negllh,hessian = se,pdf = gh.pdf,
>          tmp.data = data, transf = transform, const.pars = vars[!opt.pars],
>          silent = silent, par.names = names(vars), ...))
>
> param.est = gh.fit$par
>
> In the above, vega are the parameters to estimate and pdf is the GH   
>  pdf. This seems to work well for the case where observations are    
> equally weighted. However, I'm stuck on how to include a weighted    
> vector (w_i) to turn this problem into a weighted ML optimization.
>
> Would you please be able to suggest a function or change in code    
> which may allow me to do this?
>
> Thank you in advance for your time.
>
> Jason
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