EconPapers    
Economics at your fingertips  
 

The Catline for Deep Regression

Mia Hubert and Peter Rousseeuw ()

Journal of Multivariate Analysis, 1998, vol. 66, issue 2, 270-296

Abstract: Motivated by the notion of regression depth (Rousseeuw and Hubert, 1996) we introduce thecatline, a new method for simple linear regression. At any bivariate data setZn={(xi, yi);i=1, ..., n} its regression depth is at leastn/3. This lower bound is attained for data lying on a convex or concave curve, whereas for perfectly linear data the catline attains a depth ofn. We construct anO(n log n) algorithm for the catline, so it can be computed fast in practice. The catline is Fisher-consistent at any linear modely=[beta]x+[alpha]+ein which the error distribution satisfies med(e  x)=0, which encompasses skewed and/or heteroscedastic errors. The breakdown value of the catline is 1/3, and its influence function is bounded. At the bivariate gaussian distribution its asymptotic relative efficiency compared to theL1line is 79.3% for the slope, and 88.9% for the intercept. The finite-sample relative efficiencies are in close agreement with these values. This combination of properties makes the catline an attractive fitting method.

Keywords: algorithm; breakdown; value; heteroscedasticity; influence; function; regression; depth; robust; regression (search for similar items in EconPapers)
Date: 1998
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3) Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91751-1
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:jmvana:v:66:y:1998:i:2:p:270-296

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

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Haili He ().

 
Page updated 2020-09-12
Handle: RePEc:eee:jmvana:v:66:y:1998:i:2:p:270-296