SYMMETRY AND LATTICE CONDITIONAL INDEPENDENCE IN A MULTIVARIATE NORMAL DISTRIBUTION

A class of multivariate normal models with symmetry restrictions given by a finite group and conditional independence restrictions given by a finite distributive lattice is defined and studied. The statistical properties of these models including maximum likelihood inference, invariance and hypothesis testing are discussed.

[1]  D. Votaw.  Testing Compound Symmetry in a Normal Multivariate Distribution , 1948 .

[2]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[3]  Nicolas Bourbaki,et al.  Eléments de Mathématique , 1964 .

[4]  C. Khatri.  Classical Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution , 1965 .

[5]  Ingram Olkin,et al.  Testing and Estimation for a Circular Stationary Model , 1969 .

[6]  I. Olkin.  TESTING AND ESTIMATION FOR STRUCTURES WHICH ARE CIRCULARLY SYMMETRIC IN BLOCKS1 , 1972 .

[7]  Steen A. Andersson,et al.  Invariant Normal Models , 1975 .

[8]  J. F. C. Kingman,et al.  Information and Exponential Families in Statistical Theory , 1980 .

[9]  Steen A. Andersson,et al.  Distribution of Eigenvalues in Multivariate Statistical Analysis , 1983 .

[10]  Michael D. Perlman,et al.  Two testing problems relating the real and complex multivariate normal distributions , 1984 .

[11]  N. Wermuth,et al.  Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative , 1989 .

[12]  S. Lauritzen,et al.  Mixed graphical association models; discussions and reply , 1989 .

[13]  A. Bertelsen.  On Non-Null Distributions Connected with Testing Reality of a Complex Normal Distribution , 1989 .

[14]  S. A. Andersson.  The lattice structure of orthogonal linear models and orthogonal variance component models , 1990 .

[15]  J. N. R. Jeffers,et al.  Graphical Models in Applied Multivariate Statistics. , 1990 .

[16]  M. Frydenberg.  The chain graph Markov property , 1990 .

[17]  Jens Ledet Jensen,et al.  A Large Deviation-Type Approximation for the “Box Class” of Likelihood Ratio Criteria , 1991 .

[18]  N. Wermuth,et al.  Linear Dependencies Represented by Chain Graphs , 1993 .

[19]  Michael D. Perlman,et al.  Lattice Models for Conditional Independence in a Multivariate Normal Distribution , 1993 .

[20]  M. Perlman,et al.  Normal linear models with lattice conditional independence restrictions , 1994 .

[21]  Testing lattice conditional independence models , 1995 .

[22]  Malene Højbjerre,et al.  Lecture Notes in Statistics 101: Linear and Graphical Models for the Multivariate Complex Normal Distribution , 1995 .

[23]  M. Perlman,et al.  Normal Linear Regression Models With Recursive Graphical Markov Structure , 1998 .