Nonnegative Minimum Biased Quadratic Estimation in Mixed Linear Models

Stanislaw Gnot and Mariusz Grzadziel

Journal of Multivariate Analysis, 2002, vol. 80, issue 2, 217-233

Abstract: The problem of nonnegative quadratic estimation of a parametric function [gamma]([beta], [sigma])=[beta]'F[beta]+[summation operator]ri=1 fi[sigma]2i in a general mixed linear model {y, X[beta], V([sigma])=[summation operator]ri=1 [sigma]2iVi} is discussed. Necessary and sufficient conditions are given for y'A0y to be a minimum biased estimator for [gamma]. It is shown how to formulate the problem of finding a nonnegative minimium biased estimator of [gamma] as a conic optimization problem, which can be efficiently solved using convex optimization techniques. Models with two variance components are considered in detail. Some applications to one-way classification mixed models are given. For these models minimum biased estimators with minimum norms for square of expectation [beta]2 and for [sigma]21 are presented in explicit forms.

Keywords: mixed; linear; model; quadratic; estimation; nonnegative; minimum; biased; estimators; mean; squared; error; one-way; classification; model; symmetric; cone; primal-dual; interior-point; method (search for similar items in EconPapers)
Date: 2002
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(00)91979-1
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:80:y:2002:i:2:p:217-233

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 ().