Parameters not empirically identifiable or distinguishable, including correlation between Gaussian observations

Christian Hennig

Statistical Papers, 2024, vol. 65, issue 2, No 10, 794 pages

Abstract: Abstract It is shown that some theoretically identifiable parameters cannot be empirically identified, meaning that no consistent estimator of them can exist. An important example is a constant correlation between Gaussian observations (in presence of such correlation not even the mean can be empirically identified). Empirical identifiability and three versions of empirical distinguishability are defined. Two different constant correlations between Gaussian observations cannot even be empirically distinguished. A further example are cluster membership parameters in k-means clustering. Several existing results in the literature are connected to the new framework. General conditions are discussed under which independence can be distinguished from dependence.

Keywords: Independence testing; Random effect; Estimability; K-means clustering; Model assumptions; 62F99; 62G99 (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-023-01414-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01414-3

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-023-01414-3

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().