Maximum Likelihood Estimation of a Linear Regression Function with Grouped Data

J. G. Fryer and R. J. Pethybridge

Journal of the Royal Statistical Society Series C, 1972, vol. 21, issue 2, 142-154

Abstract: When the data in a linear regression problem come in grouped form, finding the maximum likelihood estimates of the parameters usually calls for considerable computational effort. An alternative to the fully grouped solution is to place the observations at the mid‐points of their groups, and then regard the resultant mid‐points as the observed data. Calculations for this approximate mid‐point (a.m.p.) solution here are very simple, of course. A natural conjecture is that the two kinds of estimate will not differ greatly if there are a large number of groups. We confirm this conjecture here using some data that are jointly normally distributed, though it does seem that a very fine mesh indeed is needed if all parameter estimates are to be tolerably close. But this is not the main aim of the paper. In practice, the data will often be far too coarse to allow us to use the a.m.p. estimate itself and our primary aim, again for normal data, is to show how this simple a.m.p. estimate can be “corrected” with very little effort to bring it back into line with the fully grouped maximum likelihood estimate. Consideration is also given to the adequate approximation of the estimated variance of the grouped estimate. Finally, we have calculated the grouped maximum likelihood, a.m.p. and corrected a.m.p. estimates and some associated estimated variances for a particular body of data to see how things work out in practice.

Date: 1972
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://doi.org/10.2307/2346486

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:bla:jorssc:v:21:y:1972:i:2:p:142-154

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9876

Access Statistics for this article

Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith

More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().