While there are numerous sources that *help* one understand the difference [pros and cons], there also is a paper at my Web site under the Services tab [at the bottom] entitled "Statistical Alternatives: Sturdy Statistics" that might be of interest.
WMB Statistical Services mailto:[EMAIL PROTECTED] http://home.earthlink.net/~statmanz ======================================= [EMAIL PROTECTED] (Herman Rubin) wrote in message news:<[EMAIL PROTECTED]>... > 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. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
