Re: MLE

N@poleone wrote:
David Jones wrote:

Not sure you'll find anything simple for anything beyond the simplest
case ... the uniform distribution with variable bounds.

You need to write the LL as a function of the parameters, where this
gives a separate expression depending on whether the parameters are in
certain ranges with respect to the observations. For each of these
ranges maximise the expression : typically you will find the maximum
on one of the boundaries. You would then need to find the maximum of
all these terms. You might consider just applying an auotmatic
computerised search procedure, provided you are careful with invalid
parameter combinations.

David Jones

Sorry, but I don't understand very well, maybe because of my English,
or because of I've litlle basis of statistics...
However, my problem is to construct one kernel density tree from a
sample set. In an article i read that the leaf's density is given from
the quotient of the sum of all weights of all samples that fall in the
leaf, divided by the volume (size) of the leaf. Now, how can I know the
volume of the leaf??
In the same article it specifies that it is the MLE in object...
From what you say I've understood that this MLE is the maximum between
all of weights of the samples?? Or I mistake??

Is this what you mean by a piecwise constant density:
Given k intervals (a_i,b_i] with b_i <= a_(i+1),
let p_i = P(a_i < x <= b_i), with p_i > 0 and sum p_i = 1.
Then f(x) = sum[I[a_i < x <= b_i]*p_i/(b_i - a_i)],
where I[.] is the indicator function. (To make the intervals
contiguous, change the restriction b_i <= a_(i+1) to b_i = a_(i+1).)

.

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