# English, Article, Journal or magazine article edition: Modeling Concentration and Dispersion in Multiple Regression Rolf Aaberge; Steinar Bjerve and Kjell Doksum

#### User activity

##### Share to:

Bookmark: http://trove.nla.gov.au/version/41674
Physical Description
• preprint
Language
• English

### Edition details

Title
• Modeling Concentration and Dispersion in Multiple Regression
Author
• Rolf Aaberge
• Steinar Bjerve and Kjell Doksum
Physical Description
• preprint
Notes
• We consider concepts and models that are useful for measuring how strongly the distribution of a positive response Y is concentrated near a value with a focus on how concentration varies as a function of covariates. We combine ideas from statistics, economics and reliability theory. Lorenz introduced a device for measuring inequality in the distribution of incomes that indicate how much the incomes below the uth quantile fall short of the egalitarian situation where everyone has the same income. Gini introduced an index that is the average over u of the difference between the Lorenz curve and its values in the egalitarian case. More generally, we can think of the Lorenz and Gini concepts as measures of concentration that applies to other response variables in addition to incomes, e.g. wealth, sales, dividends, taxes, test scores, precipitation, and crop yield. In this paper we propose modified versions of the Lorenz and Gini measures of concentration that we relate to statistical concepts of dispersion. Moreover, we consider the situation where the measures of concentration/​dispersion are functions of covariates. We consider the estimation of these functions for parametric models and a semiparametric model involving regression coefficients and an unknown baseline distribution. In this semiparametric model, which combines ideas from Pareto, Lehmann and Cox, we find partial likelihood estimates of the regression coefficients and the baseline distribution that can be used to construct estimates of the various measures of concentration/​dispersion.
• Spread; concentration; Lorenz curve; Gini index; Lehmann model; Cox regression; Pareto model.
• RePEc:ssb:dispap:412
Language
• English
Contributed by
OAIster

## Get this edition

• Set up My libraries

### How do I set up "My libraries"?

In order to set up a list of libraries that you have access to, you must first login or sign up. Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen.

• All (1)
• Unknown (1)
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.

## User activity

#### Tags

What are tags? Add a tag

e.g. test cricket, Perth (WA), "Parkes, Henry"

Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes.

Be the first to add a tag for this edition