Abstract:
In Ken Brewer's book, Brewer(2002), he made a strong argument for the ubiquitous presence of a specific range of the coefficient of heteroscedasticity when modeling for 'survey populations.' Basically, if each y-value were a cluster of smaller ones, the variance within the cluster would generally increase with larger predicted-y-values, in a systematic fashion. Thus the variance of , or of , tends to be larger for larger predicted-y-values. (Here we often use as a substitute for .) So why don't we always see or discuss this heteroscedasticity? Here it is argued that there are several reasons: (1) Often it is not obvious, but it is there. (2) Often there is heteroscedasticity in the estimated residuals, but it is not considered important to the application. (3) It may be countered by model and/or data issues, which effectively reduce the coefficient of heteroscedasticity. Or (4) you may be looking at an example using artificial data designed to be homoscedastic. The point is that the dominance of OLS regression may be largely due to habit. Some informal papers have been placed on ResearchGate, under a "project" covering various issues related to this, as well as the estimation of the coefficient of heteroscedasticity in regression, which is another topic that was of interest to Ken Brewer, and sometimes may be used to definitively determine when there is heteroscedasticity and approximately to what degree. These issues are discussed here.
Page(s):
315-367
DOI:
DOI not available
Published:
Journal: Pakistan Journal of Statistics, Volume: 37, Issue: 4, Year: 2021
Keywords:
predictedy
,
ideal predictedy
,
essential heteroscedasticity
,
coefficient of heteroscedasticity
,
achieved predictedy
,
Cluster
,
measure of size