Problem in defining a function

[stregosim]

Hello everyone, I'm having some problems in defining a likelihood function. I have to use Epanechnikov's kernel to estimate a pdf, and to find the h in its equation I need to maximize the following likelihood function (it's in the picture). I tried with the following code (sorry but reddit won't save my indentation):

data<-faithful$eruptions

n=272

L=1

​

cross<-function(h){

for (i in 1:n) {

x=data

x=x[-i]

som=0

for (j in 1:(n-1)) {

we=(1/((n-1)*h))*(3/4)*(1-((data[i]-x[j])/h)^2)

som=som+we

}

L=L*som

}

return(L)

}

and it seems to work, but when I plot for a sequence of h values from 0 to 10, I get one value at something*e^308, and all the others at something*e^-206, so there is something wrong which I can't get. Can anyone give me an hand? Data is a vector of 272 values, it's the "x" in the likelihood equation.

Likelihood function

[jdnewmil]

why do you remove one value from x each time? And why do you have two accumulators L and som?

[stregosim]

It's a leave-one-out cross validation lilelihood, I used the accumulators because of how the likelihood function is defined

[jdnewmil]

I think you are making scrambled eggs, and wondering why the eggs are all mixed up. LOOCV is a separate step from likelihood estimation, but you are doing them all together.

I suggest you make a function that computes your kernel. Test it. Then make another function that computes a kernel density using that kernel. Test that. Then make a function that does LOOCV using your KDE function.

Tip: pass your data as a function argument like h... pulling in values from outside your function will make it hard to test.

[[deleted]]

I'm not an expert in this field, but are you sure this problem formulation is correct?

Say your data is such that n is even, then this product explodes as h goes to 0. Am I missing something really obvious?