Exactly what is being modelled by the systematic component in a heteroscedastic linear regression

Stephen Portnoy and A. H. Welsh

Statistics & Probability Letters, 1992, vol. 13, issue 4, 253-258

Abstract: The distribution of the stochastic component of semi- and non-parametric models is often assumed to belong to a large class of distributions. In such models, the identifiability of the structural component of the model becomes important. For example, in the location problem, the class is restricted to symmetric distributions so that the parameter is always identifiable (as the center of symmetry). In linear regression problems, the slope parameters are identifiable even if the distributions are asymmetric. However, if in addition the errors in the regression model are not identically distributed, the slope parameters are not identifiable. This means that in practice large biases (which do not necessarily vanish with increasing sample size) occur. These biases arise from the difference between the distribution functional (e.g., the mean or median) which is being modelled by structural linearity and the functional being estimated by the statistical procedure used. The possible extent of this bias is illustrated here. The conclusion: it does matter what functional of the distribution is being modelled because this determines which estimator should be used.

Keywords: Bias; heteroscedasticity; linear; model; slope; parameter (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(92)90031-Y
Full text for ScienceDirect subscribers only

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:eee:stapro:v:13:y:1992:i:4:p:253-258

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().