Talk:Statistical model

message: The article Statistical assumption makes very little sense.  It claims that there are "non-modelling assumptions".  Yet the set of statistical assumptions is the statistical model.  
The reference given in the article [McPherson, 1990 (Section 3.3)] states the following.
The vast majority of statistical models require the assumption that the sample which provides the data has been selected by a process of random selection…. The importance of this assumption is made apparent in Chapter 5.
Where the sample members are not independently selected, there is a need to assume a structure or mechanism by which observations made on the sample members are connected. Generally, the statistical description is difficult even though the experimental description may be simple. For example, where plants are competing for light, moisture or nutrients, a strong growing plant is likely to be surrounded by weaker plants because of competition. Attempting to model the effects of this competition is not an easy task and frequently leads to the introduction of parameters of unknown value into the model.
Note the repeated use of the term "model".  
The valid parts of the article Statistical assumption should be merged into the article Statistical model.  FlagrantUsername (talk) 17:44, 8 November 2014 (UTC)
replies: text: It has now been over two months since the merge was proposed, and there are no comments.  So, I have left the article Statistical assumption unmerged, but substantially edited the article to make things clearer.   FlagrantUsername (talk) 15:18, 17 January 2015 (UTC)
thread_title:  Proposed merge with [[Statistical assumption]] 

message: The example is somewhat useful but loses its tractability when things get formal. The sample space S is fine, defined like that, as is \Theta. What is P_{\theta}, though? Without that information (i.e. a formula), a novice reader is lost. Neither can the mapping P_{\theta} be derived from information contained in the example (indeed, one would need to know the distribution of ages at the very least), nor can \mathcal{P} be determined in the absence of the mapping. Can anyone work out the example in more detail?Athenray (talk) 08:49, 4 September 2015 (UTC)
replies: text: I have revised the example, so that it includes a distribution of the ages. FlagrantUsername (talk) 10:39, 28 October 2017 (UTC)
thread_title:  Example 

message: I have removed the higlighted part in the following statement, which was later restored by an IP user.
: A statistical model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, "a model is a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).
My reason for removing was is that I can't see the connection between the quotation and the preceding sentence. There is no mention of statistical models, random variables, or non-random variables in the quotation. If this should be kept in the article, it needs to be explained better. Elektrolurch (talk) 10:17, 20 June 2017 (UTC)
replies: text: The quotation is indeed about statistical models, but that was not clear from the way that it was quoted. I have restored the quotation, but revised the way that it is quoted, so as to make that clear. Additionally, the citation note now includes a direct link to the page of the book that contains the quote. About the connection with the preceding sentence, mathematical equations are a formal representation. 86.183.239.72 (talk) 11:09, 24 July 2017 (UTC)
thread_title:  Removed quotation 

message: A statistical model is a special class of mathematical model. What distinguishes a statistical model from other mathematical models is that a statistical model is non-deterministic. Thus, in a statistical model specified via mathematical equations, some of the variables do not have specific values, but instead have probability distributions; i.e. some of the variables are stochastic. In the above example with children's heights, ε is a stochastic variable; without that stochastic variable, the model would be deterministic.
The above statement is confusing. Even without the error ε, the age and the height remain random variables. So the presence of random variables in the model does not turn a mathematical model into a statistical model. But what does?
AVM2019 (talk) 20:26, 22 December 2019 (UTC)
thread_title:  General remarks section 

message: A statistical model is semiparametric if it has both finite-dimensional and infinite-dimensional parameters.  Formally, if  is the dimension of \Theta and  is the number of samples, both semiparametric and nonparametric models have k \rightarrow \infty as n \rightarrow \infty.  If k/n \rightarrow 0 as n \rightarrow \infty, then the model is semiparametric; otherwise, the model is nonparametric.
1) Why should k change when the size of the sample changes? It seems that a model should have a fixed definition, and the statistician can take as many sample points as he wants in order to test the model or estimate its parameters.
If there is some pragmatic principle whereby the statistician chooses larger models when he anticipates larger samples, this should be explained in advance, not implicitly assumed.
In any case, from a mathematical perspective, in the cited text, the property semiparametric is not a property of a statistical model, but of an infinite sequence of pairs (model, sample size).   
2) The two characterizations
:A statistical model is semiparametric if it has both finite-dimensional and infinite-dimensional parameters.
and
:If k/n \rightarrow 0 as n \rightarrow \infty, then the model is semiparametric; otherwise, the model is nonparametric.
are not consistent with each other. It is true that something is finite and something is infinite in both cases; that is all they have in common.
2A02:1210:2642:4A00:C9E4:9F6:5E99:526E (talk) 18:12, 23 June 2023 (UTC)
thread_title:  Seems inconsistent with itself and with the definition