Robust estimation in the linear model with asymmetric error distributions

J. R. Collins, J. N. Sheahan and Z. Zheng

Journal of Multivariate Analysis, 1986, vol. 20, issue 2, 220-243

Abstract: In the linear model Xn - 1 = Cn - p[theta]p - 1 + En - 1, Huber's theory of robust estimation of the regression vector [theta]p - 1 is adapted for two models for the partially specified common distribution F of the i.i.d. components of the error vector En - 1. In the first model considered, the restriction of F to a set [-a0, b0] is a standard normal distribution contaminated, with probability [var epsilon], by an unknown distribution symmetric about 0. In the second model, the restriction of F to [-a0, b0] is completely specified (and perhaps asymmetrical). In both models, the distribution of F outside the set [-a0, b0] is completely unspecified. For both models, consistent and asymptotically normal M-estimators of [theta]p - 1 are constructed, under mild regularity conditions on the sequence of design matrices {Cn - p}. Also, in both models, M-estimators are found which minimize the maximal mean-squared error. The optimal M-estimators have influence curves which vanish off compact sets.

Keywords: robust; estimation; robust; regression; M-estimators; linear; model; asymmetric; distributions (search for similar items in EconPapers)
Date: 1986
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(86)90079-5
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:20:y:1986:i:2:p:220-243

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 Catherine Liu ().