Recurrence formula for expectations of products of quadratic forms

被引：9

作者：

Ghazal, GA ^{[1
]}

机构：

[1] CAIRO UNIV,INST STAT,ORMAN,GIZA,EGYPT

来源：

STATISTICS & PROBABILITY LETTERS | 1996年 / 27卷 / 02期

关键词：

covariance matrices; expectations; product of quadratic forms; random discriminants; Vandermonde determinants;

D O I：

10.1016/0167-7152(95)00050-X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we derive a recurrence formula for evaluating mathematical expectations of X'A(1)XX'A(2)X ... X'A(n)X, where X similar to N-p(0,Phi) and A(j), j = 1, 2, ..., n are (p x p) nonstochastic symmetric matrices. Subsequently, this recurrence formula is applied to some specific problems. Various related results will also be reported.

引用

页码：101 / 109

页数：9

共 19 条

[1]

Don F. J. H., 1979, Statistica Neerlandica, V33, P73

[2]

DOROGOVTEV AA, 1986, UKRANIAN MATH J, V38, P230

[3] MOMENTS OF THE RATIO OF 2 DEPENDENT QUADRATIC-FORMS [J].

GHAZAL, GA .

STATISTICS & PROBABILITY LETTERS, 1994, 20 (04) :313-319

[4]

GRAYBILL FA, 1983, MATRICES APPLICATION

[5]

GURLAND J, 1956, SANKHYA, V16, P37

[6]

JOHNSON NL, 1970, DISTRIBUTIONS STATIS

[7] COMPARISON OF K-CLASS ESTIMATORS WHEN DISTURBANCES ARE SMALL [J].

KADANE, JB .

ECONOMETRICA, 1971, 39 (05) :723-&

[8]

LANCASTER HO, 1954, J ROY STAT SOC B, V16, P247

[9] RANDOM DISCRIMINANTS [J].

LU, IL ;

RICHARDS, D .

ANNALS OF STATISTICS, 1993, 21 (04) :1982-2000

[10]

Magnus J. R., 1978, STAT NEERL, V32, P201, DOI [10.1111/j.1467-9574.1978.tb01399.x, DOI 10.1111/J.1467-9574.1978.TB01399.X]

← 1 2 →