In article <[EMAIL PROTECTED]>,
Robert J. MacG. Dawson <[EMAIL PROTECTED]> wrote:
>Herman Rubin wrote:
>> >> If a model is given with a finite number of parameters
>> >> for the underlying distributions and structure, or at
>> >> worst a finite number of parameters to be estimated,
>> >> it is called "parametric". Else, it is misnamed
>> >> "non-parametric"; it should be "infinite parametric"
>> >> as a proper description of what is to be inferred
>> >> involves an infinite number of parameters.
>and later
>> Consider the estimation of a density or a spectral
>> density. Most of the approaches use a method to produce a
>> function. Now one might think that specifying a function
>> does not specify any parameters, but it actually specifies
>> infinitely many. In fact, insisting that data are normal
>> specifies infinitely many parameters.
>and
>> A parameter is anything which can be computed from full
>> knowledge of the exact model.
> The word "parameter" appears to be being used here in
>two mutually incompatible ways. The first, earlier quote is
>consistent with what I would have taken as the usual definition
>of "parameter", namely, a variable indexing a family of
>functions/distributions/what-have-you. The concept (in this
>sense) has no meaning outside this context; asking in the
>abstract "is the mean a parameter?" is like asking "is the
>group D4 isomorphic?" or "is (0,1) a local maximum"?
This is only apparent. I stated for the so-called
non-parametric inferences that
"non-parametric"; it should be "infinite parametric"
as a proper description of what is to be inferred
involves an infinite number of parameters.
On the other hand, what are called parametric models are
described by a finite number of parameters.
> (You know the joke: examiner, "Which of these three groups
>are isomorphic?" student "The first two aren't but I think the third
>one is.")
I do not see the relevance of this. Isomorphism is a
relation. When one asks for "the generators" of a group,
any set can be used.
> Thus, for instance, the mean can be a parameter of the
>N(mu, sigma^2) family, the N(mu, 1^2) family, and the U[0,A]
>family of distributions. It cannot be a parameter of the
>N(0,sigma^2) family or the U[-A,A] family - despite the fact
>that it can be calculated from the model. It and the third
>quartile together are parameters of the N(mu,sigma^2) family,
>the U[A,B] family, but not of any other family of distributions
>given above.
You are assuming that the parameters strictly vary over
the model, and are together adequate for describing the
model. This can cause major complications in descriptions.
Thus, such things as least squares are parametric procedures.
Yet unless the least important assumption, normality, is
assumed, the parameters do not provide a full description.
And it can be a major problem if one cannot call something
a variable even if it can be shown to be constant.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
