On a property of the expected value of a determinant

L. Pronzato

Statistics & Probability Letters, 1998, vol. 39, issue 2, 161-165

Abstract: Suppose that the vectors x1, ..., xN in RP are i.i.d. with some underlying distribution [mu], and consider the matrix MN=(1/N)[summation operator]Ni=1xixTi. We show that, with constant C(N, p) = N!/(Np(N - p)!) not depending on [mu], the expected value of the determinant is of MN is proportional to the determinant of the expected value of MN. This implies, in particular, that in a linear regression problem with regressors independently generated with a measure [mu], the measure maximizing the expected value of the determinant of the information matrix is D-optimal, whatever the number of observations.

Keywords: Expected; value; Determinant; Optimal; design; D-optimality; Linear; regression (search for similar items in EconPapers)
Date: 1998
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/S0167-7152(98)00057-1
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:stapro:v:39:y:1998:i:2:p:161-165

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

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().