Likelihood cross validation estimation

Hi,

I'm trying to use likelihood cross-validation method to select the bandwidth for the kernel density estimator in Matlab.

I've done something like below:

[~,~,bw] = ksdensity(DATA_I_HAVE); 
%the default bw from ksdensity function
loglik = @(xtr,xte) sum(log(ksdensity(xtr,xte,'width',h)));
v = @(h,data,cens,freq) -sum(crossval(loglik,data,'leaveout',1));
h_hat = mle(DATA_I_HAVE,'nloglf',v,'start',bw)

Can I ask whether there is a way to put those two steps (the sum of log pdf and crossval) together? Alternatively, is there a better way to obtain the optimal bw using likelihood cross-validation method in Matlab?

Thanks very much!

Hi,

I've made some changes to the code, it works now, but takes quite long time, I really appreciate if you can give some suggestions for improvement!

[~,~,bw0] = ksdensity(DATA_I_HAVE); 
h_hat = mle(DATA_I_HAVE,'nloglf',@custnloglf,'start',bw0);
function val = custnloglf(h,data,cens,freq)
val = -sum(crossval(@loglik,data,'leaveout',1));
    function ll = loglik(xtr,xte)
        ll = sum(log(ksdensity(xtr,xte,'width',h)));
    end
end

Thanks!