A Likelihood Ratio Test for Equality of Natural Parameters for Generalized Riesz Distributions

被引：0

作者：

Andersson S.A. ^{[1
]}

Crawford J.B. ^{[2
]}

机构：

[1] Department of Statistics, Indiana University, 309 N. Park Ave, Bloomington, 47408, IN

[2] Department of Mathematics, Tarleton State University, 1333, W. Washington, Stephenville, 76402, TX

来源：

Sankhya A | 2015年 / 77卷 / 1期

关键词：

Bartlett’s test; Decomposable undirected graphs; Graphical models; Likelihood ratio test; Riesz distribution; Wishart distribution.; Primary 62H15; Secondary 62H12; 62E17; 06F99;

D O I：

10.1007/s13171-014-0052-5

中图分类号：

学科分类号：

摘要：

An important classical problem is testing whether several centered multivariate normal distributions have the same covariance matrix, which is equivalent to testing that certain Wishart distributions have the same natural parameter. Wishart distributions, which are supported on sets of positive definite matrices, are a special case of generalized Riesz distributions, which are supported on sets of matrices related to the Markov properties of decomposable undirected graphs. This leads to the problem of testing whether several generalized Riesz distributions have the same natural parameter. In this paper, we derive the likelihood ratio statistic for this testing problem and find its moments. © 2014, Indian Statistical Institute.

引用

页码：186 / 210

页数：24

共 19 条

[1]

Anderson T.W., An introduction to multivariate statistical analysis, (2003)

[2]

Andersson S.A., Brons H.K., Jensen S.T., Distribution of eigenvalues in multivariate statistical analysis, Ann. Stat, 11, 2, pp. 392-415, (1983)

[3]

Andersson S.A., and Klein T., On Riesz and Wishart distributions associated with decomposable undirected graphs, J. Multivar. Anal, 101, 3, pp. 789-810, (2010)

[4]

Andersson S.A., Madigan D., and Perlman M.D., Alternative Markov properties for chain graphs, Scand. J. Stat, 28, 1, pp. 33-85, (2001)

[5]

Bartlett M.S., Properties of sufficiency and statistical tests, Proc. R. Soc. Lond, 160, A, pp. 268-282, (1937)

[6]

Bartlett M.S., Further aspects of the theory of multiple regression, Proc. Camb. Philos. Soc, 34, pp. 33-40, (1938)

[7]

Box G.E.P., A general distribution theory for a class of likelihood criteria, Biometrika, 36, pp. 317-346, (1949)

[8]

Brown G.W., On the power of the L <sub>1</sub> test for equality of several variances, Ann. Math. Statist, 10, pp. 119-128, (1939)

[9]

Frydenberg M., The chain graph Markov property, Scand. J. Stat, 17, pp. 333-353, (1990)

[10]

Hassairi A., and Lajmi S., Riesz exponential families on symmetric cones, J. Theor. Probab, 14, 4, pp. 927-948, (2001)

← 1 2 →