Re: Constrained non linear regression using ML

[Jaroslav Hajek]

On Tue, Mar 23, 2010 at 9:10 AM, Corrado <address@hidden> wrote:
> Fredrik Lingvall wrote:
>>> 3) the pdf of e is dependent on E(y)
>>>
>>
>> Note that y is your data and it is not distributed at all - it is the
>> numbers that your data recording machine gave you. The error is just
>> something you "add" because you don't have perfect knowledge of the
>> physical process that you are studying. The better your knowledge is
>> (better theory/better model) the less the error becomes.
>>
> I do not understand what you mean by y not being distributed at all.
>
> What I mean is:
>
> 1) our observation are y = {y_1,y_2,....,y_t}.
>
> 2) Each y_i can be considered as an extraction or realisation of a
> random variable Y.
>

Yes and no. It's not a simple random variable, it's dependent on an
n-dimensional vector p: Y = Y(p). In statistics this is usually called
a "random field".

> 3) This random variable Y has a distribution pdf(Y).
>

Yes, but again it is pdf(Y,p), dependent on p. If nothing else, the
mean of the distribution is changing with k.

> 4) If I build the frequency distribution of y, then this frequency
> distribution may tell me something about the distribution of Y.
>

If your y_i correspond to different vectors p_i, they're actually
samples of different random variables, and building a histogram out of
them is not really meaningful. You first have to remove the trend to
get somewhere.

-- 
RNDr. Jaroslav Hajek, PhD
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz